The inverse of $y=5^{\log x}$ is

Let $f: X \rightarrow Y$ be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $\left(f^{-1}\right)^{-1}=f$.

If $f(x) = 3x - 5$, then ${f^{ - 1}}(x)$

State with reason whether following functions have inverse $f: \{1,2,3,4\}\rightarrow\{10\}$ with $f =\{(1,10),(2,10),(3,10),(4,10)\}$

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