Question 60238: If the function defines a one-to-one function, find the inverse.
f(x) = (x+2)^3 - 8 Answer by uma(370) (Show Source):
You can put this solution on YOUR website! f(x) = (x+2)^3 - 8
Let y = (x+2)^3 - 8
To find the inverse first we interchange x and y and then solve for y.
So the given equation becomes..
x = (y+2)^3 - 8
==> x + 8 = (y+2)^3 - 8 + 8 [adding 8 to both the sides of the equality]
==> x + 8 = (y+2)^3
Taking cube root on both the sides,
(x + 8)^(1/3) = y+2
==> (x + 8)^(1/3)- 2 = y + 2 - 2 {adding -2 to both the sides]
==> (x + 8)^(1/3) - 2 = y
Thus the inverse of the given function is given by..
f^(-1)(x) = (x + 8)^(1/3)-2
Good Luck!!!
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