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Recent questions tagged ch1

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$ (iv)\quad k(x)\;=\;x^2$

asked Mar 4, 2013 by meena.p

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective$(iii)\quad h(x)\;=\;x|x| $

asked Mar 4, 2013 by meena.p

1 answer

Let A=[-1,1].Then,dicuss whether the following functions defined on A are one-one,onto or bijective:$(ii)\quad g(x)\;=\;|\;x\;|$

asked Mar 4, 2013 by meena.p

1 answer

Give an example of a map$(iii)\quad which\; is\; neither\;one-one\;nor\;onto$

asked Mar 4, 2013 by meena.p

1 answer

Give an example of a map$(ii)\quad which\;is\;not\;one-one\;but\; not\; onto$

asked Mar 4, 2013 by meena.p

1 answer

Are the following set of ordered pairs function? If so,examine whether the mapping is injective or subjective $\;\{(a,b)\;:\;a\;$ is a person,$b\;$ is an ancestor of $a\}$

asked Mar 1, 2013 by meena.p

1 answer

If , Y = $ x^4 - \ frac$ {x$^3} ${3} when denotes the number of hours worked and denotes the amount (in Rupees) earned. Then find the value of (in interval) for which the income remains increasing? Explain the importance of earning in life?

asked Jan 24, 2013 by shanthinig

0 answers

If performance of the students ‘y’ depends on the number of hours ‘x’ of hard work done per day is given by the relation. Y = 4 x -$ \frac {x^2} {2} $ Find the number of hours, the students work to have the best performance. ‘Hours of hard work are necessary for success’ Justify.

asked Jan 24, 2013 by shanthinig

0 answers

Three shopkeepers A, B, C are using polythene, handmade bags (prepared by prisoners), and newspaper’s envelope as carry bags. it is found that the shopkeepers A, B, C are using (20,30,40) , (30,40,20,) , (40,20,30) polythene , handmade bags and newspapers envelopes respectively. The shopkeepers A, B, C spent Rs.250, Rs.220 & Rs.200 on these carry bags respectively .Find the cost of each carry bags using matrices. Keeping in mind the social & environmental conditions, which shopkeeper is better? & why?

asked Jan 24, 2013 by shanthinig

0 answers

A car parking company has 500 subscribers and collects fixed charges of Rs.300 per subscriber per month. The company proposes to increase the monthly subscription and it is believed that for every increase of Re.1, one subscriber will discontinue the service. What increase will bring maximum income of the company? What values are driven by this problem?

asked Jan 24, 2013 by shanthinig

0 answers

Check whether the function f (x) =$ x^{100}$ + sin x-1 is strictly increasing or strictly decreasing or none of both on $(-1,1)$ . Should the nature of a man be like this function? Justify your answers

asked Jan 24, 2013 by shanthinig

0 answers

let A be the set of all students of class XII in a school and R be the relation, having the same *** on A, and then prove that R is an equivalence relation. Do you think, co-education may be helpful in child development and why?

asked Jan 24, 2013 by shanthinig

0 answers

Prove that $f: R → R $ is a bijection given by $f(x) = x^3+3$. Find $f ^{-1} (x)$. Does the truthfulness and honesty may have any relation?

asked Jan 24, 2013 by shanthinig

0 answers

Prove that $f: \text{R} \rightarrow \text{R}$ is a bijection given by $f(x) = x^3 + 3$. Find $f^{-1}(x)$. Does the truthfulness and honesty may have any relation?

asked Jan 24, 2013 by pady_1

0 answers

On the set N of natural numbers, define the operation * on N by mn=gcd(m,n) for all m, n$ \varepsilon$ N. Show that is commutative as well as associative.

asked Jan 23, 2013 by meena.p

0 answers

Determine which of the following functions \[f:R \rightarrow R\;are\;(a)One-One\quad(b)Onto\]\[(i)f(x)=|x|+x\]\[(ii)f(x)=x-[x]\]

asked Jan 23, 2013 by meena.p

0 answers

Let X = {1,2,3,4,5,6,7,8,9}. Let $ R_1\;andR_2$ be relations in x given by \[R_1=\{(x,y):x-y\;is\;divisible\;by\;3\}\;and\]\[R_2=\{(x,y)!\{x,y\} \varepsilon \{1,4,7\}or\{x,y\} \varepsilon \{2,5,8\}\]\[or \{x,y\} \varepsilon \{3,6,9\}\}.\; Show\; that \;R_1=R_2.\]

asked Jan 23, 2013 by meena.p

0 answers

Prove that relation R defined on the set N of natural numbers by \[x\;R\;y \Leftrightarrow 2x^2-3xy+y^2=0\] is not symmetric but it is reflexive.

asked Jan 23, 2013 by meena.p

1 answer

Show that the function $ f:N \rightarrow N$ given by $f(x) = x -(-1)^x\;for\;all\;x\; \varepsilon\;N $ is a bijection.

asked Jan 23, 2013 by meena.p

0 answers

Define a binary operation $^$ on the set A = {0,1,2,3,4,5} as \[ab=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.\]Show that zero is an identity element for this operation and each element a of the set is invertiable with 6-a being the inverse of a.

asked Jan 23, 2013 by meena.p

0 answers

Let f and g be real valued functions, such that $(fog)(x)=\cos x^3\; and\;(gof)(x)=\cos^3x,$ find the functions f and g.

asked Jan 23, 2013 by meena.p

0 answers

Let $f : A \rightarrow B$ be a given function. A relation R in the set A is given by $R = {(a,b) \varepsilon A \times A : f(a) = f(b)}.$ Check, if R is an equivalence relation.

asked Jan 23, 2013 by meena.p

1 answer

Prove that the inverse of an equivalence relation is an equivalence relation.

asked Jan 23, 2013 by meena.p

0 answers

Let N denote the set of all natural numbers and R be the relation on N x N defined by $ (a,b)R(c,d) \Leftrightarrow ad(b + c) = bc(a + d).$ Show that R is an equivalence relation on N x N.

asked Jan 23, 2013 by meena.p

1 answer

Let a relation R on the set R of real numbers defined as $(x,y)\; \varepsilon\;R \Leftrightarrow x^24xy+3y^2\;=\;0.$Show that R is reflexive but neither symmetric nor transitive.

asked Jan 23, 2013 by meena.p

0 answers

Let a relation R on the set R of real numbers be defined as $ (a,b) \varepsilon R \Leftrightarrow 1+ ab > 0 for\; all\; a, b\; \varepsilon\; R.$show that R is reflexive and symmetric but not transitive.

asked Jan 23, 2013 by meena.p

0 answers

If the function $ f\;:\;R \rightarrow A $ given by $f(x)=\frac{x^2}{x^2+1}$is surjection, find the set A.

asked Jan 23, 2013 by meena.p

0 answers

Show that the relation "congruence modulo 2" on the set Z (set of integers) is an equivalence relation. Also find the equivalence class of 1.

asked Jan 23, 2013 by meena.p

0 answers

Let $f:R_+\rightarrow[-5,\infty) $ given by $f(x)=9x^2+6x-5.$ show that f is invertiable with $ f^{-1}(y)=\frac{\sqrt{y+6}-1}{3}.$

asked Jan 23, 2013 by meena.p

1 answer

Show that the relation R on N x N defined by $(a,b)R(c,d)\;\Leftrightarrow \; a+d = b+c $is an equivalence relation.

asked Jan 23, 2013 by meena.p

0 answers

If R is a relation on a set $A(A \neq \phi),$ prove that R is symmetric iff $R^{-1} = R$

asked Jan 23, 2013 by meena.p

0 answers

If $f(x)=log \big(\frac{1+x}{1-x}\big)$ show that $f(x)+f(y)=f \big(\frac{x+y}{1+xy}\big)$

asked Jan 23, 2013 by meena.p

0 answers

Let $ f(x)=\frac{\alpha x}{x+1},x\;\neq\;-1,$ find the value of $\alpha$ such that $f(f(x))=x$

asked Jan 23, 2013 by meena.p

0 answers

Let f, g be two functions defined by \[f(x)=\frac{x}{x+1},g(x)=\frac{x}{1-x},\;then\;find\;(fog)^{-1}(x)\]

asked Jan 23, 2013 by meena.p

0 answers

Show that $\frac{1}{\sin^3x}+\cot x+\frac{1}{x^5}+x^3 $ is an odd function.

asked Jan 23, 2013 by meena.p

0 answers

If $f(x)=\frac{1+x}{1-x},$show that $f[f(\tan\theta)]= - cot\theta$

asked Jan 23, 2013 by meena.p

0 answers

If $f(x)=\frac{5x+3}{4x-5}\big(x\neq\frac{5}{4}\big),$find g(x) such that $gof(x) = x$

asked Jan 23, 2013 by meena.p

0 answers

Let $f :R \rightarrow R $ defined by $f(x) = (ax^2+b)^3$ find the function $g :R \rightarrow R $ such that $f(g(x)) = g(f(x))$

asked Jan 23, 2013 by meena.p

0 answers

Let $ \int : {R\; \rightarrow \;R}$ be a function defined by $ f(x) = x^2-3x+4,$ for all $x \in R ,$ find the value of $f^{-1}(2)$.

asked Jan 23, 2013 by meena.p

0 answers

Let A = {4,5,0}. Find the number of binary operations that can be defined on A.

asked Jan 22, 2013 by meena.p

0 answers

Find the number of One-One functions from a finite set A to A, where n(A) = P

asked Jan 22, 2013 by meena.p

0 answers

Let * be a binary operation on the set of real numbers. If a * b = a+b-ab, 2 * ( 3 * x ) = -7, find the value of x.

asked Jan 22, 2013 by meena.p

1 answer

If $f(x)=\sin^2x+\sin^2\big(x+\frac{\pi}{3}\big)+\cos x.cos\big(x+\frac{\pi}{3}\big)\;and\;g\big(\frac{5}{4}\big)=1$, then find the value of gof(x)=x.

asked Jan 22, 2013 by meena.p

0 answers

If $f(x)=\frac{x-1}{x+1},(x \neq 1,-1),$ show that $fof^{-1}$ is an identity function.

asked Jan 22, 2013 by meena.p

0 answers

Let n be a fixed positive integer.Define a relation R in Z as follows: a,b E\inE Z, aRb if and only if a-b is divisible by n. Show that R is an equivalence relation.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: A binary operation on a set has always the identity element.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Every function is invertible.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The composition of functions is associative

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The composition of functions is commutative.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The relation R on the set A={1,2,3} defined as R={(1,1),(1,2),(2,1),(3,3)} is reflexive,symmetric and transitive.

asked Dec 20, 2012 by sreemathi.v

1 answer

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