Question

Graph the function and its inverse f(x)=x^2-4

Answer 1

Inverse function:
`y=√(x+4)`

Explanation:

• An inverse function
  `f^(-1)` is a function such
  `f^(-1)(f(x))=x`, for all x.
• In practice, to find the inverse function, we just have to swich "x" by "y" in the original function, and clear y, which would be the inverse funtion.
• In this case,
  `y=f(x)=x^2-4`. Then, if we swich x by y, we have the following expression:
  `x=y^2-4`. Now, we just have to clear y, as a function of x, by doing the following:

1. Add 2 both sides of the equation. This would yield
   `x+4=y^2`.
2. Take square root both sides of the equation. This would yield
   `y=√(x+4)`. Then we have the inverse function!
3. To verify the process, we replace f(x) (our original expression) into the new equation
   `f^(-1)(f(x))=x`, and check that equals x:
   `f^(-1)` is
   `f^(-1)(f(x))=√((x^2-4)+4) =√(x^2) =x`