If $f: \mathbb{R} \to \mathbb{R}$ is defined by $f(x) = 3x - 4$,then ${f^{ - 1}}: \mathbb{R} \to \mathbb{R}$ is

Which of the following functions cannot have their inverse defined? (where $[.] \to$ greatest integer function)

Let $f: R - \{3\} \rightarrow R - \{1\}$ be defined by $f(x) = \frac{x-2}{x-3}$. Let $g: R \rightarrow R$ be given as $g(x) = 2x - 3$. Then,the sum of all the values of $x$ for which $f^{-1}(x) + g^{-1}(x) = \frac{13}{2}$ is equal to ...... .

If $g$ is the inverse of the function $f(x)$ and $g(x) = x + \tan x$,then $f^{\prime}(x) = $

$f: R \rightarrow R, f(x) = 3x + 2$ and $g: R \rightarrow R, g(x) = 6x + 5$. Find the value of $(g \circ f^{-1})(10)$.

Consider $f: R \rightarrow R$ given by $f(x)=4x+3$. Show that $f$ is invertible. Find the inverse of $f$.