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

Consider the function $f = \{(1,2), (2,1), (3,1)\}$. Is $f$ invertible?

Let $f: R \rightarrow R, g: R \rightarrow R$ and $h: R \rightarrow R$ be differentiable functions such that $f(x)=x^3+3x+2, g(f(x))=x$ and $h(g(g(x)))=x$ for all $x \in R$. Then

Let $f: A \rightarrow B$ and $g: B \rightarrow A$ be defined as $f(x)=x^2 \forall x \in A$ and $g(x)=x^{1/2} \forall x \in B$. $f(x)$ and $g(x)$ are inverse functions to each other when

Let $e^{f(x)} = \ln x$. If $g(x)$ is the inverse function of $f(x)$,then $g'(x)$ is equal to:

Consider $f: R_{+} \rightarrow [4, \infty)$ given by $f(x) = x^{2} + 4$. Show that $f$ is invertible with the inverse $f^{-1}$ of $f$ given by $f^{-1}(y) = \sqrt{y - 4}$,where $R_{+}$ is the set of all non-negative real numbers.