If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$f ( x ) = \sqrt [ 3 ] { x + 2 }$$
A) $f ^ { - 1 } ( x ) = ( x + 2 ) ^ { 3 }$
B) $f ^ { - 1 } ( x ) = ( x - 2 ) ^ { 3 }$
C) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 2$
D) $f ^ { - 1 } ( x ) = x ^ { 3 } - 2$

Question

Quizplus · Accepted Answer

The function $f(x) = \sqrt[3]{x + 2}$ is one-to-one because every input $x$ produces a unique output, and its inverse can be found by solving for $x$ in terms of $y$. If $y = \sqrt[3]{x + 2}$, then cubing both sides gives $y^3 = x + 2$, and solving for $x$ gives $x = y^3 - 2$, which corresponds to $f^{-1}(x) = x^3 - 2$.

If the Function Is One-To-One, Find Its Inverse f(x)=x+23f ( x ) = \sqrt [ 3 ] { x + 2 }f(x)=3x+2​

If the Function Is One-To-One, Find Its Inverse $f ( x ) = \sqrt [ 3 ] { x + 2 }$