Recent questions in Relations and Functions

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

True or False: Let A={0,1} and N be the set of natural numbers.Then the mapping $f:N \rightarrow A$ defined by f(2n-1)=0,f(2n)=1, $\quad n\in N$ ,is onto.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: An integer m is said to be related to another integer n if m is a integral multiple of n.This relation in Z is reflexive,symmetric and transitive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Every relation which is symmetric and transitive is also reflexive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let $f:R \rightarrow R$ be the function defined by f(x)=sin (3x+2) $\quad x\in R$ .Then f is invertible.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let R={(3,1),(1,3),(3,3)} be a relation defined on the set A={1,2,3}.Then R is symmetric,transitive but not reflexive.

asked Dec 20, 2012 by sreemathi.v

1 answer

If $f(x)=(4-(x-7)^3\},then\;f^{-1}(x)$ =____________.

asked Dec 20, 2012 by sreemathi.v

1 answer