Question 164342
Given: {{{f(x) = -2x+3}}} find the inverse {{{f^(-1)(x)}}}
{{{f(x) = -2x+3}}} First, replace the f(x) with y to get:
{{{y = -2x+3}}} Now exchange the x and y to get:
{{{x = -2y+3}}} Now solve this for y by subtracting 3 from both sides.
{{{x-3 = -2y}}} Divide both sides by -2.
{{{(x-3)/-2 = y}}} Now replace the y with {{{f^(-1)(x)}}} to get:
{{{highlight(f^(-1)(x) = -(x-3)/2)}}}
Check:
{{{f(f^(-1)(x)) = -2(-(x-3)/2)+3}}} 
{{{f(f^(-1)(x)) = (x-3)+3}}}
{{{f(f^(-1)(x)) = x}}}