In general, a function is invertible only if each input has a unique output. That is, each output is paired with exactly one input. That way, when the mapping is reversed, it will still be a function!
How do you know if a function is invertible?
Finding the Inverse of a Function
- 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.
What function is not invertible?
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function. Step 2: Make the function invertible by restricting the domain.
