Find the inverse of the function.
-$$f ( x ) = 5 x ^ { 3 } + 7$$
A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 7 } { 5 } }$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x + 7 } { 5 } }$
C) Not a one-to-one function
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } } { 5 } } - 7$

Question

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = 5x^3 + 7$, you solve for $x$ in terms of $y$. Swap $x$ and $y$, getting $x = 5y^3 + 7$. Solve for $y$, which gives $y = \sqrt[3]{\frac{x - 7}{5}}$, making option A correct.

Find the Inverse of the Function f(x)=5x3+7f ( x ) = 5 x ^ { 3 } + 7f(x)=5x3+7

Find the Inverse of the Function $f ( x ) = 5 x ^ { 3 } + 7$