If f(x) =√(x) +3 , what is the equation for f–1(x)?

Question

If f(x) =
`√(x) +3` , what is the equation for f–1(x)?

Answer 1

Answer:
`f^(-1)(x) = (x-3)^2`

Explanation:

We are given that
`f(x) = √(x) + 3`. A trick to solve for the inverse is to switch the f(x) and x in the equation. This gives us

`x = √(f(x)) + 3`

Now, we can solve for this f(x) which gives us

`x = √(f(x)) + 3\\x -3 = √(f(x))\\(x -3)^2 = f(x)`

Then we simply let that
`f(x)` be
`f^(-1)(x)`. Thus, we have
`f^(-1)(x) = (x-3)^2`