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Questions >> JEEMAIN and NEET >> Mathematics >> Class12 >> Relations and Functions

The inverse of $f(x)=x-[x],$ where $[x]$ is greatest integer function is

answered Sep 29, 2019 by pranav.awasarmol123

2 answers

If $f_k(x) = \large\frac{1}{k}$ $(\sin^k x + \cos^k x)$ , where $x\in R$ and $k \geq 1$ . The $f_4(x) - f_6(x)$ equals

answered Nov 15, 2017 by ityagi002

1 answer

f(xy)=f(x)+f(y) . Then Prove that f(x) =Klog(x) where k is constant

answered Dec 17, 2014 by pady_1

1 answer

If $a\in R$ and the equation $-3 (x-[x])^2 + 2(x-[x])+a^2 = 0$ , (where $[x]$ denotes the greatest integer $\leq x$ ) has no integral solution, then all possible values lie in the interval:

asked Apr 6, 2014 by balaji.thirumalai

0 answers

The identity element of the binary operation $\large $ defined on $Q-\{0\}$ as $a\large $ $b=\large\frac{ab}{2},$ $\forall \:a,b\:\in\:Q-\{0\}$

answered May 31, 2013 by rvidyagovindarajan_1

1 answer

If a relation $R$ on the set $\{1,2,3\}$ is defined as $R=\{(1,2)\}$ , then $R$ is

answered May 31, 2013 by rvidyagovindarajan_1

1 answer

If $f:[0,1]\rightarrow\:[0,1]$ is defined as $f(x)=\left \{\begin {array}{c,c}x &if\:x\:is\:rational\\1-x & if\:x\:is\:irrational\end {array}\right.$ then $fof(x)=?$

answered May 31, 2013 by rvidyagovindarajan_1

1 answer

The number of bijection mappings that are possible from $Set \:A$ containing 5 elements to $Set\:B$ containing 6 elements is ?

answered May 31, 2013 by rvidyagovindarajan_1

1 answer

The maximum number of equivalence relations on the set $A=\{1,2,3\}$ is?

answered May 31, 2013 by rvidyagovindarajan_1

1 answer

Find the domain of $f(x)=\sqrt{cos(sinx)}+sin^{-1}\bigg(\large\frac{1+x^2}{2x}\bigg)$

answered May 30, 2013 by rvidyagovindarajan_1

1 answer

Find the domain of $sin(log(\large\frac{\sqrt{4-x^2}}{1-x}))$

answered May 30, 2013 by rvidyagovindarajan_1

1 answer

Which of the following pairs of functions are equal ?

answered May 30, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is such that $f(x+y)=f(x).f(y)$ , then $f(0)$ = ?

answered May 30, 2013 by rvidyagovindarajan_1

1 answer

If function $f(x)$ is given by
$\small\left|\begin {array} {c,c,c} -cos(x+x^2) & -sin(x+x^2) & cos(x+x^2)\\sin(x^2-x) & -cos(x^2-x) & sin(x^2-x)\\sin2x &0 &sin2x^2 \end {array}\right|$ , then find $f(0)$

answered May 30, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2\},$ then how many binary operations having 1 as identity and 2 as inverse of 2 are possible?

answered May 29, 2013 by rvidyagovindarajan_1

1 answer

If a set $A$ has 2 elements, then how many binary operations are possible in $A$ ?

answered May 29, 2013 by rvidyagovindarajan_1

1 answer

If $g(x)=x^2+x-2\:\:and\:\:\large\frac{1}{2}$ $gof(x)=2x^2-5x+2$ then $f(x)= ?$

answered May 28, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined as $f(x)=[x]^2+[x+1]-3$ where $[x]$ is greatest integer of $x$ , then what type of function is $f$ ?

answered May 28, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=\left\{\begin{array}{c,c} |x| &x \leq 1 \\2-x &x>1\end{array}\right.$ , then $fof(x)=?$

answered May 28, 2013 by rvidyagovindarajan_1

1 answer

If $f:A\rightarrow B$ is defined as $f(x)=\sqrt 3 sinx+cosx+4$ and $f$ is invertible then find A.

answered May 28, 2013 by rvidyagovindarajan_1

1 answer

The value of $a\:\:and\:\:b$ for which $f:R\rightarrow R$ is defined as $f(x)=ax+b$ where $a,b\in R$ is bijection with $fof$ as its identity is ?

answered May 28, 2013 by rvidyagovindarajan_1

1 answer

Find the linear functions that maps $[-1,1]$ onto $[0,2]$ .

answered May 28, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2,3,4\}\:and\:B=\{3,4,7\}$ then the no. of onto functions from $A\rightarrow B$ =?

answered May 27, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R\:\:and\:\:f(x)=|x|$ and $A=(0,1)$ , then find $f^{-1}(A)$

answered May 27, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=x^n$ , $n\in N$ and $gof(x)=ng(x)$ , then $g(x)$ = ?

answered May 27, 2013 by rvidyagovindarajan_1

1 answer

$If A\{x,y,z\},\:\:B=\{1,2,3\}$ and $f:A\rightarrow B\:\:is\:1-1\:$ function. Also one out of the following statements, $f(z)\neq 2,\:\:f(x)=1\:\:and\:\:f(y)\neq 1$ is true. then $f^{-1}(1)=?$

answered May 25, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{x:x\in R\:and\:x\geq 1\}$ and $f:A\rightarrow A$ is defined as $f(x)=2^{x(x-1)},$ then find $f^{-1}(x).$

answered May 25, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined as $f(x)=6^x+6^{|x|}$ then what type of function is $f$ ?

answered May 25, 2013 by rvidyagovindarajan_1

1 answer

If $f(X)=\large\frac{kx}{1+x}$ , $x\neq1$ and $fof(x)=x$ , then find $k$ .

answered May 25, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{-1,0,1\}$ and $f:A\rightarrow A$ is defined as $f(x)=x^2$ , then what type of function is $f$ ?

answered May 25, 2013 by rvidyagovindarajan_1

1 answer

If $log_2(log_3(log_4(log_5x)))=0$ then x= ?

answered May 18, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=\cos \log x$ then $f(x).f(y)-\large\frac{1}{2}$ $\bigg(f(\large\frac{x}{y}$ ) $+f(xy)\bigg)= ?$

answered May 18, 2013 by rvidyagovindarajan_1

1 answer

$f:N\rightarrow Z$ is a function defined as $f(n)=\left\{ \begin {array} {1 1} \large\frac{n-1}{2}, \:\:when\:\: n\:\: is\:\: odd \\ -\large \frac{n}{2},\:\:when\:\: n\:\: is\:\: even \\ \end{array} \right.$ , then $f$ is

answered May 13, 2013 by rvidyagovindarajan_1

1 answer

If $M$ is the set of all $2\times 2$ matrices with real entries and $f :M\rightarrow R$ is defined as $f(A)=|A| \:\forall\:A\in M$ , then $f$ is

answered May 12, 2013 by rvidyagovindarajan_1

1 answer

If $g(x)=1+x-[x]$ where $[x]$ is greatest integer $x$ and $f(x)=\left\{\begin{array}{111}-1,\:\:\:\:x<0\\0,\:\:\:\:\:x=0\\1,\:\:\:\:\:x>0\end{array}\right.$ then $fog(x)=?$

answered May 12, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=x^2\:\:and\:\:g(x)=2^x$ and $fog(x)=gof(x)$ then $x$ = ?

answered May 12, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=\large\frac{1}{1-x}$ is a function defined in $R-\{1\}$ then $\;fofof(x)$ = ?

answered May 12, 2013 by rvidyagovindarajan_1

1 answer

If $$ is a binary operation defined as $ab=3a-b$ , then $(23)4=$ ?

answered May 12, 2013 by rvidyagovindarajan_1

1 answer

If * is a binary operation defined by a*b= $\frac{ab}{100}$ in $Q^+$ then the inverse element of 0.1 is:

answered May 12, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=x^2$ $g(x)=sinx$ , $\forall x\in R$ , then the set of all $x$ satisfying $fogogof(x)=gogof(x)$ is

answered May 7, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)$ is a real valued function satisfying $f(x+1)+f(x-1)=2f(x)$ $\forall x\in R$ and $f(0)=0$ , then for any $n\in N,\:f(n)$ = ?

answered May 7, 2013 by rvidyagovindarajan_1

1 answer

The domain of $y=sin^{-1}(1+3x+2x^2)$ is

answered May 7, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow S$ defined by $\:f(x)=\sin x-\sqrt3\; \cos x+1\;$ is onto function then $S$ = ?

answered May 4, 2013 by rvidyagovindarajan_1

1 answer

The value of $\alpha$ for which the function $f(x)=1+\alpha x,\:\:\alpha\neq 0$ is the inverse of itself is:

answered May 4, 2013 by rvidyagovindarajan_1

1 answer

What is the inverse of the function $f(x)=\large\frac{e^x-e^{-x}}{e^x+e^{-x}}$

answered May 2, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2,3\}$ then the no. of relations in $A$ containing $(1,2)$ and $(1,3)$ which are reflexive and symmetric but not transitive is

answered May 1, 2013 by rvidyagovindarajan_1

1 answer

If * is binary operation defined in N as ab= $a^3+b^3$ then is

answered May 1, 2013 by rvidyagovindarajan_1

1 answer

If n(A) = 4, n(B) = 6, then the number of 1-1 functions from A to B is

answered May 1, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2,3,4\}$ and $B=\{1,2\}$ , then the number of onto functions from $A$ to $B$ is

answered Apr 28, 2013 by rvidyagovindarajan_1

1 answer

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