If $f: R \rightarrow R$ is defined by $f(x)=x^{3}$,then $f^{-1}(8)$ is equal to

If the function $f : R \to R$ is defined by $f(x) = \log_a(x + \sqrt{x^2 + 1})$,where $(a > 0, a \neq 1)$,then $f^{-1}(x)$ is

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

Let $f(x) = (x - 1)^2 + 1$ for $x \ge 1$.
Statement-$1$: $S = \{x : f(x) = f^{-1}(x)\} = \{1, 2\}$.
Statement-$2$: $f$ is a bijection and $f^{-1}(x) = 1 + \sqrt{x - 1}$ for $x \ge 1$.

If $f(x) = \frac{x}{1 + x}$,then ${f^{-1}}(x)$ is equal to

Let $f(x) = x^3 + 8x + 3$. Which one of the properties of the derivative enables you to conclude that $f(x)$ has an inverse?