Which of the following functions is inverse of itself
Which of the following functions is inverse of itself
- A
$f(x) = \frac{{1 - x}}{{1 + x}}$
- B
$f(x) = {5^{\log x}}$
- C
$f(x) = {2^{x(x - 1)}}$
- D
None of these
Similar Questions
Let $f: W \rightarrow W$ be defined as $f(n)=n-1,$ if is odd and $f(n)=n+1,$ if $n$ is even. Show that $f$ is invertible. Find the inverse of $f$. Here, $W$ is the set of all whole numbers.
Let $f: W \rightarrow W$ be defined as $f(n)=n-1,$ if is odd and $f(n)=n+1,$ if $n$ is even. Show that $f$ is invertible. Find the inverse of $f$. Here, $W$ is the set of all whole numbers.
Which of the following functions cannot have their inverse defined ? (where $[.]\, \to$ greatest integer function)
Which of the following functions cannot have their inverse defined ? (where $[.]\, \to$ greatest integer function)
Let f : $R \to R$ be defined by $f\left( x \right) = \ln \left( {x + \sqrt {{x^2} + 1} } \right)$ , then number of solutions of $\left| {{f^{ - 1}}\left( x \right)} \right| = {e^{ - \left| x \right|}}$ is
Let f : $R \to R$ be defined by $f\left( x \right) = \ln \left( {x + \sqrt {{x^2} + 1} } \right)$ , then number of solutions of $\left| {{f^{ - 1}}\left( x \right)} \right| = {e^{ - \left| x \right|}}$ is
Consider $f: R \rightarrow R$ given by $f(x)=4 x+3 .$ Show that $f$ is invertible. Find the inverse of $f$
Consider $f: R \rightarrow R$ given by $f(x)=4 x+3 .$ Show that $f$ is invertible. Find the inverse of $f$
Let $Y =\left\{n^{2}: n \in N \right\} \subset N .$ Consider $f: N \rightarrow Y$ as $f(n)=n^{2}$ Show that $f$ is invertible. Find the inverse of $f$
Let $Y =\left\{n^{2}: n \in N \right\} \subset N .$ Consider $f: N \rightarrow Y$ as $f(n)=n^{2}$ Show that $f$ is invertible. Find the inverse of $f$