Find the inverse function of f.

Question

f(x) =

36 − x2
, 0 ≤ x ≤ 6

I can't seem to find this inverse, someone help please?

Answer 1

consider the parabola y=36-x^2
Its vertex is at (0,6)
So, restricting the domain to 0<=x<=6 means we only want the right branch of the function.

SO, the inverse function is found the usual way, by switching variables and solving for y:

x = 36-y^2
y^2 = 36-x
y = ±√(36-x)

but, we have restricted the domain of f to 0<=x<=6, so that means that the inverse of f is just

y = +√(36-x)