Find the Inverse f(x) = cube root of x/9-4

Problem

ƒ(x)=√(3,x/9−4)

Solution

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

y=√(3,x/9−4)

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

x=√(3,y/9−4)

3. Cube both sides of the equation to eliminate the cube root.

x3=y/9−4

4. Isolate the term containing y by adding 4 to both sides.

x3+4=y/9

5. Solve for y by multiplying both sides of the equation by 9

9*(x3+4)=y

6. Distribute the 9 and replace y with the inverse notation ƒ(x)(−1)

ƒ(x)(−1)=9*x3+36

Final Answer

ƒ(x)(−1)=9*x3+36

Want more problems? Check here!