Write an equation of the inverse for the one-to-one function $$f ( x ) = 5 x ^ { 3 } - 5$$
A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 5 } { 5 } }$
B) $f ^ { - 1 } ( x ) = \left( \frac { x + 5 } { 5 } \right) ^ { 3 }$
C) $f ^ { - 1 } ( x ) = \frac { x - 5 } { 5 }$
D) $f ^ { - 1 } ( x ) = \frac { x + 5 } { 5 }$

Question

Write an equation of the inverse for the one-to-one function $$f ( x ) = 5 x ^ { 3 } - 5$$ 
A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 5 } { 5 } }$
B) $f ^ { - 1 } ( x ) = \left( \frac { x + 5 } { 5 } \right) ^ { 3 }$
C) $f ^ { - 1 } ( x ) = \frac { x - 5 } { 5 }$
D) $f ^ { - 1 } ( x ) = \frac { x + 5 } { 5 }$

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$, then solve for $y$. Starting with $y = 5x^3 - 5$, swapping gives $x = 5y^3 - 5$. Solving for $y$ gives $y = \sqrt[3]{\frac{x + 5}{5}}$, which matches choice A.

Write an Equation of the Inverse for the One-To-One Function f(x)=5x3−5f ( x ) = 5 x ^ { 3 } - 5f(x)=5x3−5

Write an Equation of the Inverse for the One-To-One Function $f ( x ) = 5 x ^ { 3 } - 5$