Find the reflection $f(x)$ and the invers reflection of$ f(x)$

Question

With the given reflection \begin{align} f(7x-5)=2x-1 \end{align} How would I find this reflection, any orientation would be appreciated!

Answer 1

hint: $ u = 7x-5 \implies f(u) = 2\left(\dfrac{u+5}{7}\right) - 1 = \dfrac{2u+10}{7} - 1= \dfrac{2u+3}{7}\implies f(x) = \dfrac{2x+3}{7}$. To find the inverse, switch $x$ and $y$ in the last equation we have: $x = \dfrac{2y+3}{7} \implies y = \dfrac{7x-3}{2} = f^{-1}(x)$.