Question

Find f ^ -1 (1) of f (x) = 2x - 3/3 - x

Answer 1

$\displaystyle f(x)=\frac{2x-3}{3-x}\\y=\frac{2x-3}{3-x}\\y(3-x)=2x-3\\3y-xy=2x-3\\-xy-2x=-3-3y\\xy+2x=3+3y\\x(y+2)=3+3y\\x=\frac{3+3y}{y+2}\\f^{-1}(x)=\frac{3+3x}{x+2}\\\\f^{-1}(1)=\frac{3+3(1)}{1+2}\\f^{-1}(1)=\frac{6}{3}\\\boxed{\boxed{f^{-1}(1)=2}}$