Find the inverse function of f.
$f ( x ) = x ^ { 9 } - 2$
A) $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x } - 2$
B) $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } - 2$
C) $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x - 2 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x + 2 }$
E) $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } + 2$

Question

Find the inverse function of f. 
$f ( x ) = x ^ { 9 } - 2$
A) $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x } - 2$
B) $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } - 2$
C) $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x - 2 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x + 2 }$
E) $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } + 2$

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = x^9 - 2$, we swap to get $x = y^9 - 2$, and then solve for $y$ to get $y = \sqrt[9]{x + 2}$.

Find the Inverse Function of F f(x)=x9−2f ( x ) = x ^ { 9 } - 2f(x)=x9−2

Find the Inverse Function of F $f ( x ) = x ^ { 9 } - 2$