SOLUTION: Find the inverse of each function. Is the inverse a function? f(x)=(x+2)^2-4 f(x)=4x^3-1

Question 186433: Find the inverse of each function. Is the inverse a function?

f(x)=(x+2)^2-4

f(x)=4x^3-1
Answer by feliz1965(151) (Show Source): You can put this solution on YOUR website!
I will do one and you can do the other.
Find the inverse of f(x)= 4x^3-1.
First, let f(x) = y.
y = 4x^3 - 1
Now switch places with x and y.
x = 4y^3 - 1
Next, solve for y.
x + 1 = 4y^3
(x + 1)/4 = y^3
Taking the cube root of each side we get:
cuberoot{(x + 1)/4)} = y
We now replace y with the inverse function notation f^(-1)x.
f^(-1)x = cuberoot{(x + 1)/4)} and it is a function.

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