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

Problem

ƒ(x)=6*x3−3

Solution

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

y=6*x3−3

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

x=6*y3−3

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

x+3=6*y3

4. Divide both sides by 6 to isolate the cubic term.

(x+3)/6=y3

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

y=√(3,(x+3)/6)

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

ƒ(x)(−1)=√(3,(x+3)/6)

Final Answer

ƒ(x)(−1)=√(3,(x+3)/6)

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