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.
