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


Please help 20 points !

Answer:

C

Step-by-step explanation:

We are given the function:

[tex]f(x)=y=5x^3-6[/tex]

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:

[tex]y=5x^3-6[/tex]

Switching the two variables:

[tex]x=5y^3-6[/tex]

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

[tex]x+6=5y^3[/tex]

Dividing both sides by 5:

[tex]\displaystyle y^3=\frac{x+6}{5}[/tex]

And taking the cube root of both sides:

[tex]\displaystyle y=\sqrt[3]{\frac{x+6}{5}}[/tex]

Thus:

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

Our answer is C.

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