Find the Inverse (x+2)^3-8

Problem

ƒ(x)=(x+2)3−8

Solution

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

y=(x+2)3−8

2. Interchange the variables x and y to begin finding the inverse relationship.

x=(y+2)3−8

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

x+8=(y+2)3

4. Apply the cube root to both sides to eliminate the exponent.

√(3,x+8)=y+2

5. Solve for y by subtracting 2 from both sides.

y=√(3,x+8)−2

6. Rewrite the result using inverse function notation ƒ(x)(−1)

ƒ(x)(−1)=√(3,x+8)−2

Final Answer

ƒ(x)(−1)=√(3,x+8)−2

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