If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { - \frac{5}{3}} \right) - (fog)\left( { - \frac{5}{3}} \right) = $
$1$
$-1$
$2$
$4$
If $f:[1,\; + \infty ) \to [2,\; + \infty )$ is given by $f(x) = x + \frac{1}{x}$ then ${f^{ - 1}}$ equals
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
Let $f: N \rightarrow Y $ be a function defined as $f(x)=4 x+3,$ where, $Y =\{y \in N : y=4 x+3$ for some $x \in N \} .$ Show that $f$ is invertible. Find the inverse.
Let $f:\left[ {4,\infty } \right) \to \left[ {1,\infty } \right)$ be a function defined by $f\left( x \right) = {5^{x\left( {x - 4} \right)}}$ then $f^{-1}(x)$ is