Image about $y=x$ ?

$\begin{aligned} f(x) & = \frac{17}{x} \\ \Rightarrow f^{-1} \left( \frac{17}{x} \right) & = x \quad \quad \small \color{#3D99F6}{\text{Let } y = \frac{17}{x} \quad \Rightarrow x = \frac{17}{y}} \\ \Rightarrow f^{-1} (y) & = \frac{17}{y} \end{aligned}$

$\quad \space \space \Rightarrow \boxed{f^{-1} (x) = \dfrac{17}{x}}$

To find the inverse, let $y=f(x)$ . As soon as we have the function in the form $x=~...$ then we swap the $x$ and $y$ letters round and we have our inverse function. Therefore:

$y=\dfrac{17}{x}$

$\Rightarrow x=\dfrac{17}{y}$

$\Rightarrow {f}^{-1}(x)=\large \color{#20A900}{\boxed{\dfrac{17}{x}}}$

We know f(x)=17/x. substituting x=f^-1(x), we have f( f^-1(x))=17/f^-1(x) =x . ==>f^-1(x)=17/x.