The inverse of the function $\frac{{{{10}^x} - {{10}^{ - x}}}}{{{{10}^x} + {{10}^{ - x}}}}$ is
$\frac{1}{2}{\log _{10}}\left( {\frac{{1 + x}}{{1 - x}}} \right)$
$\frac{1}{2}{\log _{10}}\left( {\frac{{1 - x}}{{1 + x}}} \right)$
$\frac{1}{4}{\log _{10}}\left( {\frac{{2x}}{{2 - x}}} \right)$
None of these
Which of the following functions is inverse of itself
Consider $f: R \rightarrow R$ given by $f(x)=4 x+3 .$ Show that $f$ is invertible. Find the inverse of $f$
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
If $f : R \to R, f(x) = x^2 + 1$, then $f^{-1}(17)$ and $f^{-1}(-3)$ are
If the function $f : R \to R$ is defined by $f(x) = log_a(x + \sqrt {x^2 +1} ), (a > 0, a \neq 1)$, then $f^{-1}(x)$ is