Find the Inverse f(x)=x^3-8

Problem

ƒ(x)=x3−8

Solution

1. Replace ƒ(x) with y to set up the equation for the inverse.

y=x3−8

2. Interchange the variables x and y to begin solving for the inverse function.

x=y3−8

3. Isolate the term containing y by adding 8 to both sides of the equation.

x+8=y3

4. Solve for y by taking the cube root of both sides.

y=√(3,x+8)

5. Replace y with the inverse function notation ƒ(x)(−1)

ƒ(x)(−1)=√(3,x+8)

Final Answer

ƒ(x)(−1)=√(3,x+8)

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