If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then by definition of inverse function,
[tex]f\left(f^{-1}(x)\right) = x[/tex]
so that
[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 x2 + 5}[/tex]
