Question

Given f(x) = (5x + 1) / 2

Solve for f^-1(8)

Please help :(

Answer 1

y=(5x+1)/2 => x=(2y-1)/5
=> f^(-1)(x) = (2x-1)/5
f^(-1)(8) = 3

Answer 2

\(\bf f(x)={\color{blue}{ y}}=\cfrac{5{\color{brown}{ x}}+1}{2}\qquad inverse\implies {\color{brown}{ x}}=\cfrac{5{\color{blue}{ y}}+1}{2}\leftarrow f^{-1}(x)
\\ \quad \\
\textit{solve for "y", and then set x=8, that is }f^{-1}(8)\)

notice that to find the "inverse relation", we simply swap about the variables, and then solve for "y"