Question

Let f(x)=x^2 - 16. find f^-1(x).

Answer 1

A quadratic function doesn't have inverse function. But you can find inverse function for each of its "arms".


`f(x)=x^2-16 \Rightarrow x_(vertex)=0\\ y=x^2-16\\ x^2=y+16\\ x=-√(y+16) \vee x=√(y+16)\\ f^(-1)(x)=-√(x+16) \hbox{ for } x<0\hbox{ (left arm)}\\ f^(-1)(x)=√(x+16) \hbox{ for } x>0\hbox{ (right arm)}`

Answer 2

`f(x)=x^2-16\\\\y=x^2-16\\\\x^2=y+16\\\\x=√(y+16)\\\\f^(-1)(x)=√(x+16)`