If a function $f: R \rightarrow R$ is defined by $f(x) = \frac{4x}{5} + 3$,then $f^{-1}(x) =$

If $g(x)$ is the inverse function of $f(x)$, where $f(x) = \frac{5x + 3}{4x - 1}$, then $g(1) = $

If the function $f:[1, \infty) \to [1, \infty)$ is defined by $f(x) = 2^{x(x - 1)}$,then $f^{-1}(x)$ is

Which of the following functions is an invertible function?

$f(x) = \sin x + \cos x, g(x) = x^2 - 1$. Then $g(f(x))$ is invertible if:

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