Find the inverse of the function.
-$$f ( x ) = 5 x ^ { 3 } + 6$$
A) Not a one-to-one function
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x } { 5 } } - 6$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } + 6 } { 5 } }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 6 } { 5 } }$

Question

Quizplus · Accepted Answer

The inverse of the function $f(x) = 5x^3 + 6$ is found by solving for $x$ in terms of $y$. Set $y = 5x^3 + 6$, then solve for $x$: $x = \sqrt[3]{\frac{y - 6}{5}}$. Thus, the inverse function is $f^{-1}(x) = \sqrt[3]{\frac{x - 6}{5}}$.

Find the Inverse of the Function f(x)=5x3+6f ( x ) = 5 x ^ { 3 } + 6f(x)=5x3+6

Find the Inverse of the Function $f ( x ) = 5 x ^ { 3 } + 6$