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Answers posted by thanvigandhi_1
Questions
3013
answers
0
best answers
0
votes
Draw the graph for the following constant function: f(x) = 2 for all x $ \in $ R
answered
Jun 28, 2014
https://clay6.com/mpaimg/15i.jpg
0
votes
Draw the graph of the identity function f: R $ \rightarrow $ R : f(x) = x for all x $ \in $R.
answered
Jun 28, 2014
Graph of f(x) = xhttps://clay6.com/mpaimg/14.jpg
0
votes
Find the domain and ranges of the following real valued functions $ f(x) = \sqrt{9-x^2}$
answered
Jun 28, 2014
Domain of f is [– 3, 3], Range of f = [0, 3]
0
votes
Find the domain and range of the following real valued function. $ f(x) = \large\frac{2+x}{2-x}$
answered
Jun 28, 2014
Domain of f is R – {2} , Range of f is R – {– 1},
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votes
Find the Range of $ f (x) = ^{(7 – x)}P_{x – 3}$.
answered
Jun 27, 2014
{1, 3, 2}
0
votes
Find the Domain of $ f (x) = ^{(7 – x)}P_{x – 3}. $
answered
Jun 27, 2014
{3, 4, 5}
0
votes
Find the Domain of $f(x) = \large\frac{3}{\sqrt{5+x}+\sqrt{5-x}}$
answered
Jun 27, 2014
(– 5, 5)
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votes
What is the range of the function $ f(x) = \large\frac{5x-1}{2x+7}$ defined on its maximum domain?
answered
Jun 27, 2014
Range of f = R - $ \bigg\{ \large\frac{ 5}{2} \bigg\}$
0
votes
Find the domain of the real function $f(x) = \sqrt{1-{\sqrt{2-}\sqrt{3-x}}}$
answered
Jun 27, 2014
–1 $ \leq $ x $ \leq $ 2.
0
votes
Let A = {–1, 2, 2, – 4} and $B = \bigg\{ -\large\frac{1}{4}$$, -1, \large\frac{1}{2}$$, 1, 2 \bigg\}$ \[\] If f = {(x, y) | xy =1, x $ \in $ A, y $ \in $ B}, prove that ‘f’ is a function from ‘A’ to ‘B’. Also, find its domain, range and co-domain.
answered
Jun 27, 2014
Domain of ‘f’ = the set of first members of the ordered pairs in ‘f’ = {–1, 2, –4} Range of ‘f’ =
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votes
Let A = {–1, 2, 2, – 4} and $B = \bigg\{ -\large\frac{1}{4}$$, -1, \large\frac{1}{2}$$, 1, 2 \bigg\}$ \[\] Is f = {(– 1, – 1), (2, 1), (– 4, 2)} a function from ‘A’ to ‘B’? If so, find its domain, range and co-domain.
answered
Jun 27, 2014
Domain of ‘f’ = the set of first members of the ordered pairs in ‘f’ = {–1, 2, –4}, Range of f = t
0
votes
Let f : A $ \rightarrow $ R be a real function. A $ \subseteq$ R such that f(x) $ \sqrt{x-2}$ . Then find Range of ‘f’
answered
Jun 27, 2014
Range of f = $ R^+ $
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votes
Let f : A $ \rightarrow $ R be a real function. A $ \subseteq$ R such that f(x) $ \sqrt{x-2}$ . Then find Domain of ‘f’
answered
Jun 27, 2014
Domain of f = {x : x /x $ \geq $ 2, x $ \in $ R$^+$} (since if x < 2, f(x) will be an imaginary ...
0
votes
Let f : A $ \rightarrow $ R be a real function. A $ \subseteq$ R such that f(x) $ \sqrt{x-2}$ . Then find ‘a’ if f(a) = 2
answered
Jun 27, 2014
a=6
0
votes
Let f : A $ \rightarrow $ R be a real function. A $ \subseteq $ R such that f(x) $ \sqrt{x-2}$ . Then find f(11)
answered
Jun 27, 2014
f(11) =$ \pm $3
0
votes
If $ f(x) = 1 –\large\frac{1}{x}$ , find $f \bigg[ f \bigg(\large\frac{1}{x} \bigg) \bigg]$.
answered
Jun 27, 2014
$ \large\frac{x}{x-1}$
0
votes
Let f(x) = $x^2$ + 2x + 3. Find $ \large\frac{f(x+h)-f(c)}{h}$ where h $ \neq $ 0.
answered
Jun 27, 2014
(2x + h + 2)
0
votes
Let f: R –{1} $ \rightarrow $ R be defined by $ f(x) = \large\frac{x+1}{x-1}$ where x $\neq $ 1. Find f(2), f $ \bigg( \large\frac{1}{2} \bigg)$ , f($ \pi $), f(3) and f $ \bigg( \large\frac{1}{3} \bigg)$
answered
Jun 27, 2014
$f(2) = 1, f(1/2) = -3,f ( \pi )= \large\frac{x+1}{x-1}$$ , f(3)=2 \: f \bigg( \large\frac{1}{3} \b...
0
votes
Let A = {–2, –1, 0, 1}, B = {1, 2, 3, 4} and ‘f’ is a subset of A × B, given by f = {(x, y) | x + y =1}. Is ‘f’ a function from ‘A’ to ‘B’? If not, remove minimum number of elements from the set ‘A’, so that ‘f’ may be a function from the new set to ‘B’.
answered
Jun 27, 2014
‘f’ is not a function from ‘A’ to ‘B’. If the element ‘1’ is removed from the set ‘A’, we have the
0
votes
Is the relation a function or not? Why?
answered
Jun 27, 2014
‘f’ is not a function.
0
votes
Suppose A = {a, b, c}; B = {x, y, z}. A rule ‘f’ is given by f(a) = x; f(b) = y; f(c) = y. Is ‘f’ a function from ‘A’ to ‘B’?
answered
Jun 27, 2014
It is a function from ‘A’ to ‘B’.
0
votes
Find the range of each of the following functions.\[\] (i) f(x) = 2 – 3x, x $ \in $ R, x > 0 \[\] (ii) f(x) = $x^2$ + 2, x, is a real number. \[\] (iii) f(x) = x, x is a real number
answered
Jun 27, 2014
(i) (-$ \infty $, 2) (ii) [2, $ \infty $) (iii) R
0
votes
The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $ t(c) = \large\frac{9c}{5}$$+32$. Find the value of C, when t(C) = 212
answered
Jun 27, 2014
100
0
votes
The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $ t(c) = \large\frac{9c}{5}$$+32$. Find t(-10)
answered
Jun 27, 2014
14
0
votes
The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $ t(c) = \large\frac{9c}{5}$$+32$. Find t(28)
answered
Jun 27, 2014
$ \large\frac{412}{5}$
0
votes
The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $ t(c) = \large\frac{9c}{5}$$+32$. Find t(0)
answered
Jun 27, 2014
32
0
votes
A function f is defined by f(x) = 2x – 5. Write down the values of \[\] (i) f(0), (ii) f(7), (iii) f(–3)
answered
Jun 27, 2014
(i) –5 (ii) 9 (iii) –11
0
votes
Find the domain and range of the following real function: $f(x) = \sqrt{9-x^2}$
answered
Jun 27, 2014
Domain of f(x) is {x : –3 ≤ x ≤ 3} or [–3, 3], Range of f(x) is {x: 0 ≤ x ≤ 3} or [0, 3].
0
votes
Find the domain and range of the following real function: f(x) = –|x|
answered
Jun 27, 2014
Domain of f is R, Range of f is (-$ \infty $, 0].
0
votes
Whether the following relation is function? Give reason. If it is a function, determine its domain and range. {(1, 3), (1, 5), (2, 5)}
answered
Jun 27, 2014
Not a function.
0
votes
Whether the following relation is function? Give reason. If it is a function, determine its domain and range.{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
answered
Jun 27, 2014
Function. Here, domain = {2, 4, 6, 8, 10, 12, 14} and range = {1, 2, 3, 4, 5, 6, 7}
0
votes
Wether the following relation is function? Give reason. If it is a function, determine its domain and range. \[\] {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
answered
Jun 27, 2014
Function. Here, domain = {2, 5, 8, 11, 14, 17} and range = {1}
0
votes
Let f(x) = and g(x) = $ \sqrt x$ be two functions defined over the set of non-negative real numbers. Find (f + g) (x), (f – g) (x), (fg) (x) and $ \bigg( \large\frac{f}{g} \bigg) (x)$.
answered
Jun 26, 2014
We have (f + g) (x) = $ \sqrt x + x, (f-g) (x) = \sqrt x - x$$(fg)x= \sqrt x (x)=x^{\large\frac{...
0
votes
Let f(x) = $x^2$ and g(x) = 2x + 1 be two real functions. Find $ (f + g) (x), (f –g) (x), (fg) (x), \bigg( \large\frac{f}{g} \bigg) (x)$
answered
Jun 26, 2014
We have, f + g (x) = f(x) + g(x) = $x^2$ + 2x + 1, Similarly (f –g) (x) = $x^2$ – 2x – 1, (fg) (x)
0
votes
Define the real valued function f: R – {0} $ \rightarrow $ R defined by $f(x) = \large\frac{1}{x}$ x $ \in $ R –{0}. Complete the Table given below using this definition. What is the domain and range of this function?
answered
Jun 26, 2014
The completed Table is given byhttps://clay6.com/mpaimg/15ans.jpgThe domain is all real numbers exce...
0
votes
Draw the graph of the function f : R $ \rightarrow $ R defined by f (x) = $x^3$, x $ \in $ R.
answered
Jun 26, 2014
We have f(0) = 0, f(1) = 1, f(–1) = –1, f(2) = 8, f(–2) = –8, f(3) = 27; f(–3) = –27, etc.Therefore
0
votes
Define the function f: R $ \rightarrow $ R by y = f(x) = $x^2$, x $ \in $ R. Complete the Table given below by using this definition. What is the domain and range of this function? Draw the graph of f.
answered
Jun 26, 2014
The completed Table is given below:https://clay6.com/mpaimg/ex13ans.jpgDomain of f = {x : x $ \in $ ...
0
votes
Let N be the set of natural numbers. Define a real valued function f : N $ \rightarrow $ N by f (x) = 2x + 1.Using this definition, complete the table given below.
answered
Jun 26, 2014
The completed table is given byhttps://clay6.com/mpaimg/exans.jpg
0
votes
Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not? \[\] (i) R = {(2,1),(3,1), (4,2)}, (ii) R = {(2,2),(2,4),(3,3), (4,4)} (iii) R = {(1,2),(2,3),(3,4), (4,5), (5,6), (6,7)}
answered
Jun 26, 2014
(i) Since 2, 3, 4 are the elements of domain of R having their unique images, this relation R is a ...
0
votes
Let N be the set of natural numbers and the relation R be defined on N such that R = {(x, y) : y = 2x, x, y $ \in $ N}. \[\] What is the domain, co-domain and range of R? Is this relation a function?
answered
Jun 26, 2014
The domain of R is the set of natural numbers N. The co-domain is also N. The range is the set of ev...
0
votes
What is the roster form of the relation R = {(x, y): y = $x^2$ and |x| < 3, x $ \in $ Z?
answered
Jun 26, 2014
{(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)}Hence (C) is the correct answer.
0
votes
A relation R from A to B is defined as \[\] R = {(x, y): (x − y) is a positive integer; x $ \in $ A, x $ \in $ B}, where A = {0, 1, 2, 7, 9, 13} and B = {3, 1, 2, 8}\[\] The domain and range of the relation R are respectively
answered
Jun 26, 2014
{2, 7, 9, 13} and {1, 2, 3, 8}Hence (D) is the correct answer.
0
votes
Some relations are given as \[\] $R_1$ = {(a, b), (b, c), (a, c), (c, b)} \[\] $R_2$ = {(1, 2), (2, 5), (6, 6), (3, 4)} \[\] $R_3$ = {a, p), (b, q), (p, t), (r, t)} \[\] $R_4$ = {(10, 11), (11, 12), (10, 13)} \[\] $R_5$ = {(15, 20), (20, 25), (25, 30)}\[\] Which of the given relations are not functions?
answered
Jun 26, 2014
$R_1\: and \: R_4$Hence (A) is the correct answer.
0
votes
For the set X = {1, 2, 3, …, 15}, a relation R on X is defined as R = {(x, 2x + 3): x $ \in $ X} \[\] What are the respective co-domain and range of R?
answered
Jun 26, 2014
{1, 2, …, 15} and {5, 7, 9, 11, 13, 15}Hence (D) is the correct answer.
0
votes
A relation R on the set P = {5, 6, 7, 8, 9} is defined as R = {(x, y): the sum of x and y is a multiple of 4; x, y $ \in $ P}. How can this relation be represented diagrammatically?
answered
Jun 26, 2014
Hence (D) is the correct answer.
0
votes
For a relation R from a non-empty set A to a non-empty set B, which of the following statements is always correct?
answered
Jun 26, 2014
Range of R is a subset of co-domain of R.Hence (B) is the correct answer.
0
votes
Three sets A, B, and C is given as: \[\] A = {x: x $ \in $ R, $x^2$ − 1 = 0} \[\] B = {x: x in whole number and x < 3} \[\] C = {x: x $ \in $ R and $x^2$ + 2x = 0} \[\] Which set is equal to the set (A $ \times $ B) $ \cap $ (B $ \times $ C)?
answered
Jun 26, 2014
{(1, 0)}Hence (A) is the correct answer.
0
votes
Three sets P, Q, and R under the universal set U = {1, 2, 3, 4, 5, 6, 7} are given as\[\] P = {2, 5, 7}, Q = {1, 2, 3, 4, 5}, R = {5, 6, 7}.\[\] Which of the following statements is incorrect with respect to the given sets?
answered
Jun 26, 2014
(P $ \cap $ Q) $ \times $ P = {(2, 2), (2, 5), (2, 7), (5, 5), (5, 7)Hence (D) is the correct answer...
0
votes
For set A = {−6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4}, a relation R on A is defined as \[\] R = {(x, y): (x, y) lie on the line 2x + 3y = 6, where x, y $ \in $ A}. \[\] How can the given relation R be written in roaster form?
answered
Jun 26, 2014
{(-3, 4), (0, 2), (3, 0)}Hence (B) is the correct answer.
0
votes
If two sets P and Q are defined as P = {3, 5, 7} and Q = {2, 3, 8}, then which of the following represents a possible relation from P to Q?
answered
Jun 26, 2014
$R_4$ = {(3, 3), (5, 2), (5, 3), (7, 8)}Hence (D) is the correct answer.
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