If $f:IR \to IR$ is defined by $f(x) = 3x - 4$, then ${f^{ - 1}}:IR \to IR$ is
$4 - 3x$
$\frac{{x + 4}}{3}$
$\frac{1}{{3x - 4}}$
$\frac{3}{{x + 4}}$
If the function $f:[1,\;\infty ) \to [1,\;\infty )$ is defined by $f(x) = {2^{x(x - 1)}},$ then ${f^{ - 1}} (x)$ is
State with reason whether following functions have inverse $f: \{1,2,3,4\}\rightarrow\{10\}$ with $f =\{(1,10),(2,10),(3,10),(4,10)\}$
It is easy to see that $f$ is one-one and onto, so that $f$ is invertible with the inverse $f^{-1}$ of $f$ given by $f^{-1}=\{(1,2),(2,1),(3,1)\}=f$
If $f(x) = 3x - 5$, then ${f^{ - 1}}(x)$
Let $Y =\left\{n^{2}: n \in N \right\} \subset N .$ Consider $f: N \rightarrow Y$ as $f(n)=n^{2}$ Show that $f$ is invertible. Find the inverse of $f$