Let the function $f$ be defined by $f(x) = \frac{{2x + 1}}{{1 - 3x}}$, then ${f^{ - 1}}(x)$ is
$\frac{{x - 1}}{{3x + 2}}$
$\frac{{3x + 2}}{{x - 1}}$
$\frac{{x + 1}}{{3x - 2}}$
$\frac{{2x + 1}}{{1 - 3x}}$
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 $g ( x )=2 x -3$. Then, the sum of all the values of $x$ for which $f^{-1}( x )+ g ^{-1}( x )=\frac{13}{2}$ is equal to ...... .
Let $f: N \rightarrow Y $ be a function defined as $f(x)=4 x+3,$ where, $Y =\{y \in N : y=4 x+3$ for some $x \in N \} .$ Show that $f$ is invertible. Find the inverse.
Inverse of the function $y = 2x - 3$ is
State with reason whether following functions have inverse $h:\{2,3,4,5\} \rightarrow\{7,9,11,13\}$ with $h=\{(2,7),(3,9),(4,11),(5,13)\}$
If $f : R \to R, f(x) = x^2 + 1$, then $f^{-1}(17)$ and $f^{-1}(-3)$ are