Asked by Lydia
Find the inverse function of f.
f(x) =
36 − x2
, 0 ≤ x ≤ 6
I can't seem to find this inverse, someone help please?
f(x) =
36 − x2
, 0 ≤ x ≤ 6
I can't seem to find this inverse, someone help please?
Answers
Answered by
Steve
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)
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)
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