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Recent questions tagged p11

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(ii) \(f : R\; \to R\; defined \; by \; f(x)\; =\; 1+x^2\)

asked Mar 18, 2013 by meena.p

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iv)\quad k=\{(1,4),(2,5)\} $

asked Mar 13, 2013 by sreemathi.v

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(iii)\quad h=\{(1,4),(2,5),(3,5)\} $

asked Mar 13, 2013 by sreemathi.v

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$(ii)\quad g=\{(1,4),(2,4),(3,4)\} $

asked Mar 13, 2013 by sreemathi.v

1 answer

State whether the function is one-one, onto or bijective.

$f : R\; \to R$ defined by $f(x)\; =\; 1+x^2$

asked Mar 6, 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

Is the function $ f(x)=\Large\frac{3x+4\tan x}{x}$ continuous at x = 0? If not, how may the function be defined to make it continuous at this point.

asked Jan 25, 2013 by meena.p

1 answer

Show that the function :$f(x)= \left\{ \begin{array}{1 1} \Large\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \quad when\;x\neq0 \\ 0, & \quad when\; x=0 \end{array} \right. $ is discontinuous at x = 0.

asked Jan 25, 2013 by meena.p

1 answer

Given that $ f(x)= \left\{ \begin{array}{1 1} \Large\frac{1- \cos 4x}{x^2}, & \quad if\;x<0 \\ a & \quad ,if\;x=0 \\ \Large\frac{\sqrt x}{\sqrt{16+\sqrt{x}}-4}, & \quad if\;x>0 \end{array}. \right. $ If f(x) is continuous at x = 0, find the value of a.

asked Jan 25, 2013 by meena.p

1 answer

Find $\Large \frac{dy}{dx}$ when $y=\tan^{-1}\Large\frac{1+x^2}{1-x^2}$

asked Jan 25, 2013 by meena.p

1 answer

Find $\Large \frac{dy}{dx}$ when $ y=a^x.x^a$

asked Jan 25, 2013 by meena.p

1 answer

Verify Rolles theorem for the function $f(x)=\sin 2x \;in\;\bigg[0,\Large\frac{\pi}{2}\bigg]$

asked Jan 25, 2013 by meena.p

1 answer

Let $y=y=\sqrt{e^\sqrt x },x>0\;find\;\large\frac{dy}{dx}.$

asked Jan 25, 2013 by meena.p

1 answer

If $ f(x)=\begin{vmatrix} x & x^2 & x^3 \\ 1 & 2x & 3x^2 \\ 0 & 2 & 6x \end{vmatrix}$ than find $ f' (x)$

asked Jan 25, 2013 by meena.p

1 answer

If $ f^1(x)=g(x)\;and\;g^1(x)=-f(x)$ for all n and $f(2)=f^1(2)=4,$ find the value of $f^2(24)+g^2(24)$

asked Jan 24, 2013 by meena.p

1 answer

Find the set of all points where the function f(x) = 2x |x| is differentiable.

asked Jan 24, 2013 by meena.p

1 answer

Find $ \frac{dy}{dx}\;when\;y=\Large x^{x^{x^{x.....}}}$

asked Jan 24, 2013 by meena.p

1 answer

Let f be a non zero continuous function satisfying f(x+y) = f(x).f(y) for all x, y $ \epsilon$ R. If f(2) = 9 then find the value of f(3).

asked Jan 24, 2013 by meena.p

1 answer

Let f be continuous function on [1,3]. If f takes only rational values for all x and f(2) = 10 then find the value of f(1.5)

asked Jan 24, 2013 by meena.p

1 answer

If functions $f\;:\;A \rightarrow B\;and\;g\;:\;B \rightarrow A $ satisfy g o f =$I_A$ ,then is f one-one and g onto

asked Dec 18, 2012 by sreemathi.v

1 answer

Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$\quad f=\{(1,4),(1,5),(2,4),(3,5)\} $

asked Dec 18, 2012 by sreemathi.v

1 answer

Let the function $f\;:\;R \rightarrow R$ be defined by$ f(x)=\cos x,\forall \;x\;\in R$.Show that f is neither one-one nor onto

asked Dec 18, 2012 by sreemathi.v

1 answer

Let C be the set of complex numbers.Prove that the mapping $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C,$is neither one-one nor onto.

asked Dec 18, 2012 by sreemathi.v

1 answer

If the mappings f and g are given by\[f\;=\;\{(1,2),(3,5),(4,1)\} \;and\;g=\{(2,3),(5,1),(1,3)\},write\;f\;o\;g\]

asked Dec 18, 2012 by sreemathi.v

1 answer

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

asked Dec 18, 2012 by sreemathi.v

1 answer

Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ a function?If g is described by $g(x)=\alpha x+\beta$,then what value should be assigned to $\alpha\;and\;\beta.$

asked Dec 18, 2012 by sreemathi.v

1 answer

If $f : R \rightarrow R$ is defined by $f(x)=x^2-3x+2$, write $f(f(x))$.

asked Dec 18, 2012 by sreemathi.v

1 answer

Let A={a,b,c,d} and the function f={(a,b),(b,d),(c,a),(d,c)},Write $f^{-1}$.

asked Dec 18, 2012 by sreemathi.v

1 answer

Let f : $R \to R$ be the function defined by $f(x)=2x-3$ $\forall x \in R$.Write $f^{-1}.$

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $f,g:R \rightarrow $R be defined by $f(x)=2x+1$ and $g(x)=x^2-2,\forall x \in R,$respectively. Then, find $g\;of(x)$.

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $D$ be the domain of the real valued function $f$ defined by $f(x)=\sqrt{25-x^2}.$Then, write $D$

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $A={a,b,c}$ and the relation $R$ be defined on $A$ as follows: $R= {(a,a)(b,c)(a,b)}$. Write the minimum number of ordered pairs to be ordered pairs to be added in $R$ to make $R$ reflexive and transitive.

asked Dec 18, 2012 by sreemathi.v

1 answer

Let $f:\;N\;\to N\;be\;defined\;by\;f(n)= \left\{ \begin{array}{1 1} \frac{n+1}{2}, & if\;n\;is\;odd\\ \frac{n}{2}, & if\;is\;even\end{array} \right. \qquad for\;all\;n \in N$ \[\text{state whether the function f is bijective.Justify your answer.} \]

asked Dec 10, 2012 by sreemathi.v

1 answer

Let $f : R \to R$ be defined as $f (x) = 3x$. Choose the correct answer:

asked Nov 9, 2012 by vaishali.a

1 answer

Let $f: R \to R $, be defined as $f(x) = x^4$. Choose the correct answer.

asked Nov 9, 2012 by vaishali.a

1 answer

Let $A=R-\{3\}$ and $B=R-\{1\}$. Consider the function $ f:A \to B$ defined by $f(x)=\large\frac {x-2}{ x-3}$. Is $f$ one-one and onto?

asked Nov 9, 2012 by vaishali.a

1 answer

Let \(A\) and \(B\)be sets. Show that\(f : A × B \to\; B×A\)such that \( f(a,b)\,=\,(b,a)\) is bijective function

asked Nov 8, 2012 by vaishali.a

1 answer

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(i) \(f : R\; \to R\; defined \; by \; f(x)\; =\; 3-4x\)

asked Nov 8, 2012 by vaishali.a

1 answer

Let \(A=\{1,2,3\},\; B = \{4,5,6,7\}\) and let \(f = \{(1,4),(2,5),(3,6)\}\)be a function from \(A\) to \(B\). Show that \(f\) is one-one.

asked Nov 8, 2012 by vaishali.a

1 answer

Show that the Signum Function \(f : R \to R\), given by \[ f(x) = \left\{ \begin{array}{l l} 1, & if \; x \; > 0 \\ 0, & if\; x\;= 0 \text{ is neither one-one nor onto } \\ -1, & if\; x \;< 0 \end{array} \right. \]

asked Nov 8, 2012 by vaishali.a

1 answer

Show that the Modulus Function \(f : R \to R\), given by \( f(x) = |\;x\;|\), is neither one-one nor onto, where\( |\;x\;|\; is\; x\), if \(x\) is positive or \(0\) and \(|\;x\;|\; is\; \) \(-\)\(x\), if \( x\) is negative.

asked Nov 8, 2012 by vaishali.a

1 answer

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