The inverse of $y = 5^{\log x}$ is

If $f: R \rightarrow R$ is a mapping defined by $f(x)=x^{3}+5$,then $f^{-1}(x)$ is equal to

If $f(x) = 2 + |\sin^{-1} x|$ and $A = \{x \in R : f^{-1}(x) \text{ exists} \}$,then $A = $

Suppose $f(x) = (x + 1)^2$ for $x \ge -1$. If $g(x)$ is the function whose graph is the reflection of the graph of $f(x)$ with respect to the line $y = x$,then $g(x)$ equals

State with reason whether the following function has an inverse: $f: \{1,2,3,4\} \rightarrow \{10\}$ with $f = \{(1,10), (2,10), (3,10), (4,10)\}$.

Let $f(x) = \sin x + \cos x$ and $g(x) = x^2 - 1$. Then $g(f(x))$ is invertible for $x \in $