A one-to-one function is given. Write an expression for the inverse function.
-$$f ( x ) = 4 x ^ { 3 } - 9$$
A) $f ^ { - 1 } ( x ) = \frac { x - 9 } { 4 }$
B) $f ^ { - 1 } ( x ) = \left( \frac { x + 9 } { 4 } \right) ^ { 3 }$
C) $f ^ { - 1 } ( x ) = \frac { x + 9 } { 4 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 9 } { 4 } }$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = 4x^3 - 9$, swapping gives $x = 4y^3 - 9$, and solving for $y$ gives $y = \sqrt[3]{\frac{x + 9}{4}}$.

A One-To-One Function Is Given f(x)=4x3−9f ( x ) = 4 x ^ { 3 } - 9f(x)=4x3−9

A One-To-One Function Is Given $f ( x ) = 4 x ^ { 3 } - 9$