[tex]\text{Given that,}\\\\f(x) = 2x -10\\\\\text{Write f(x) as}~ y = 2x -10\\\\\text{Replace x with y and solve for y,}\\\\x =2y-10\\\\\implies 2y = x+10\\\\\implies y= \dfrac 12 (x+10) \\\\\implies y = \dfrac 12x + 5\\\\\implies f^{-1}(x) = \dfrac 12x + 5\\\\\\\text{Hence the inverse of the given function is}~ ~\dfrac 12x + 5[/tex]
