If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = x[/tex]
by definition of inverse function. We have
[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 10 = x[/tex]
Solve for the inverse :
[tex]2f^{-1}(x) + 10 = x \\\\ 2f^{-1}(x) = x-10 \\\\ \boxed{f^{-1}(x) = \dfrac{x-10}2}[/tex]
