A one-to-one function is given. Write an expression for the inverse function.
-$$m ( x ) = 7 x ^ { 3 } + 2$$
A) $m ^ { - 1 } ( x ) = \frac { x - 2 } { 7 }$
B) $m ^ { - 1 } ( x ) = \frac { x + 2 } { 7 }$
C) $m ^ { - 1 } ( x ) = \left( \frac { x + 2 } { 7 } \right) ^ { 3 }$
D) $m ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 2 } { 7 } }$

Question

Quizplus · Accepted Answer

To find the inverse function, you swap $x$ and $y$ and solve for $y$. Starting with $y = 7x^3 + 2$, swap to get $x = 7y^3 + 2$, then solve for $y$ to get $y = \sqrt[3]{\frac{x - 2}{7}}$, which matches option D.

A One-To-One Function Is Given m(x)=7x3+2m ( x ) = 7 x ^ { 3 } + 2m(x)=7x3+2

A One-To-One Function Is Given $m ( x ) = 7 x ^ { 3 } + 2$