Question: how do you know the inverse of a function?
Answer: First, replace f(x) with y . ...  Replace every x with a y and replace every y with an x . Solve the equation from Step 2 for y . ...  Replace y with f−1(x) f − 1 ( x ) . ...  Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.