If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = x ^ { 3 } + 4$$
A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 4 }$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 4$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } - 4 }$
D) not a one-to-one

Question

Quizplus · Accepted Answer

The function $f(x) = x^3 + 4$ is one-to-one because for every x value, there is a unique y value, and it passes the horizontal line test. To find the inverse, swap x and y and solve for y: $x = y^3 + 4$, leading to $y = \sqrt[3]{x - 4}$, which matches choice C.

If the Function Is One-To-One, Find Its Inverse f(x)=x3+4f ( x ) = x ^ { 3 } + 4f(x)=x3+4

If the Function Is One-To-One, Find Its Inverse $f ( x ) = x ^ { 3 } + 4$