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To find the inverse function f(x)^-1 , we will assume"
==> x= (y-2)^1/3
==> f(x)-1= (x-2)^1/3
To find the inverse function of f(x) = x^3+2.
Let y = x^3+2. So,
y-2 = x^3. Or
x^3 = y-2. Taking cube root,
x = (y-2) ^(1/3).
Interchanging x and y , we get:
y = (x-2)^(1/3) is the inverse function of the given function.
For the beginning, we'll write:f(x)=x^3+2 as y=f(x)=x^3+2
Now, we'll solve this equation for x:
Now, we'll interchange x and y:
So, the inverse function is:
[f(x)]^(-1) = (x-2)^1/3
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