Recent questions tagged kvquestionbank2012

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

If $( x-a)^2 + (y-b)^2 = c^2$, for some $ c > 0$, prove that $\Large\frac{\begin{bmatrix} 1 + \left(\frac{dy}{dx}\right)^2 \\[0.3em] \end{bmatrix}^{\frac{\Large 3}{\Large 2}}}{\Large\frac{d^2y}{dx^2}}$is a constant independent of $a$ and $b$.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Ask Questions, Get Answers

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

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.

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}.$

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.

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

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

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

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

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

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

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

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

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 $f^{-1}(2)$.

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

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

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.

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.

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

If \(( x-a)^2 + (y-b)^2 = c^2\), for some \( c > 0\), prove that $\Large\frac{\begin{bmatrix} 1 + \left(\frac{dy}{dx}\right)^2 \\[0.3em] \end{bmatrix}^{\frac{\Large 3}{\Large 2}}}{\Large\frac{d^2y}{dx^2}}$is a constant independent of \(a\) and \(b\).

Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$