Question

For the function f(x) = 5x3 – 6, find f-1(x).


Please help 20 points !

Answer 1

C

Explanation:

We are given the function:

`f(x)=y=5x^3-6`

And we want to find its inverse.

In order to find the inverse of a function, we take the following steps:

1) Switch the independent variable x with the dependent variable y.

2) Solve for the dependent variable y.

We have:

`y=5x^3-6`

Switching the two variables:

`x=5y^3-6`

Solve for y. We will add 6 to both sides:

`x+6=5y^3`

Dividing both sides by 5:

`\displaystyle y^3=(x+6)/(5)`

And taking the cube root of both sides:

`\displaystyle y=\sqrt[3]{(x+6)/(5)}`

Thus:

`\displaystyle f^(-1)(x)=\sqrt[3]{(x+6)/(5)}`

Our answer is C.