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

State with reason whether following functions have inverse $g :\{5,6,7,8\} \rightarrow\{1,2,3,4\}$ with $g=\{(5,4),(6,3),(7,4),(8,2)\}$

Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ and $g:\{a, b, c\} \rightarrow$ $\{$ apple, ball, cat $\}$ defined as $f(1)=a$, $f(2)=b$,  $f(3)=c$,  $g(a)=$ apple, $g(b)=$ ball and $g(c)=$ cat. Show that $f,\, g$ and $gof$ are invertible. Find out $f^{-1}, \,g^{-1}$ and $(gof)^{-1}$ and show that $(gof)^{-1}=f^{-1}og^{-1}$

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 …… .

If $f : R \to R, f(x) = x^2 + 1$, then $f^{-1}(17)$ and $f^{-1}(-3)$ are