Find the inverse function of
$g ( x ) = x ^ { 8 } - 7$
A) $g ^ { - 1 } ( x ) = \sqrt [ 8 ] { x - 7 }$
B) $g ^ { - 1 } ( x ) = \sqrt [ 8 ] { x + 7 }$
C) $g ^ { - 1 } ( x ) = ( x - 7 ) ^ { 8 }$
D) $g ^ { - 1 } ( x ) = ( x + 7 ) ^ { 8 }$
E) $g ^ { - 1 } ( x ) = x ^ { 8 } + 7$

Question

Find the inverse function of 
$g ( x ) = x ^ { 8 } - 7$
A) $g ^ { - 1 } ( x ) = \sqrt [ 8 ] { x - 7 }$
B) $g ^ { - 1 } ( x ) = \sqrt [ 8 ] { x + 7 }$
C) $g ^ { - 1 } ( x ) = ( x - 7 ) ^ { 8 }$
D) $g ^ { - 1 } ( x ) = ( x + 7 ) ^ { 8 }$
E) $g ^ { - 1 } ( x ) = x ^ { 8 } + 7$

Quizplus · Accepted Answer

To find the inverse of a function, we first need to replace $g(x)$ with $y$. $$y = x^8 - 7$$ Then, we solve for $x$: $$x = \sqrt[8]{y + 7}$$ Finally, we switch $x$ and $y$ to get the inverse function: $$g^{-1}(x) = \sqrt[8]{x + 7}$$ Answer choice B matches this result.

Find the Inverse Function Of g(x)=x8−7g ( x ) = x ^ { 8 } - 7g(x)=x8−7

Find the Inverse Function Of $g ( x ) = x ^ { 8 } - 7$