If the functions $f$ and $g$ are defined by $f(x) = 3x - 4$ and $g(x) = 2 + 3x$ for $x \in R$,then $g^{-1}(f^{-1}(5))$ 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.

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

Let $f: N \rightarrow R$ be a function defined as $f(x)=4x^{2}+12x+15$. Show that $f: N \rightarrow S$,where $S$ is the range of $f$,is invertible. Find the inverse of $f$.

Let the function $f$ be defined by $f(x) = \frac{2x + 1}{1 - 3x}$,then $f^{-1}(x)$ is

Consider $f: R_{+} \rightarrow [-5, \infty)$ given by $f(x) = 9x^{2} + 6x - 5$. Show that $f$ is invertible with $f^{-1}(y) = \frac{\sqrt{y+6}-1}{3}$.