Find the Inverse f(x)=x^3-6

Problem

ƒ(x)=x3−6

Solution

1. Replace the function notation ƒ(x) with y to make the equation easier to manipulate.

y=x3−6

2. Swap the variables x and y to begin solving for the inverse relationship.

x=y3−6

3. Isolate the term containing y by adding 6 to both sides of the equation.

x+6=y3

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

y=√(3,x+6)

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

ƒ(x)(−1)=√(3,x+6)

Final Answer

ƒ(x)(−1)=√(3,x+6)

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