Question

How do you find the inverse of this function

Answer 1

$y=\dfrac{2+x}{1-\dfrac{1}{2}x}\\\\y\left(1-\dfrac{1}{2}x\right)=2+x\\\\y-\dfrac{1}{2}xy=2+x\\\\2y-xy=4+2x\\\\2x+xy=2y-4\\\\x(2+y)=2y-4\\\\x=\dfrac{2y-4}{y+2}\\\\\boxed{f^{-1}(x)=\dfrac{2x-4}{x+2}}$