Find the inverse function of
$g ( x ) = x ^ { 7 } - 4$
A) $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { x - 4 }$
B) $g ^ { - 1 } ( x ) = ( x + 4 ) ^ { 7 }$
C) $g ^ { - 1 } ( x ) = x ^ { 7 } + 4$
D) $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { x + 4 }$
E) $g ^ { - 1 } ( x ) = ( x - 4 ) ^ { 2 }$

Question

Find the inverse function of 
$g ( x ) = x ^ { 7 } - 4$ 
A) $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { x - 4 }$
B) $g ^ { - 1 } ( x ) = ( x + 4 ) ^ { 7 }$
C) $g ^ { - 1 } ( x ) = x ^ { 7 } + 4$
D) $g ^ { - 1 } ( x ) = \sqrt [ 7 ] { x + 4 }$
E) $g ^ { - 1 } ( x ) = ( x - 4 ) ^ { 2 }$

Quizplus · Accepted Answer

To find the inverse function of g(x), we need to solve for x in terms of y. 
So, starting with the given function: 
y = x^7 - 4 
Adding 4 to both sides: 
y + 4 = x^7 
Taking the 7th root of both sides: 
(x + 4)^(1/7) = y^(1/7) 
Switching x and y: 
(y + 4)^(1/7) = x^(1/7) 
Which gives us: 
g^(-1)(x) = (x + 4)^(1/7) 
Therefore, the correct answer is D.

Find the Inverse Function Of g(x)=x7−4g ( x ) = x ^ { 7 } - 4g(x)=x7−4

Find the Inverse Function Of $g ( x ) = x ^ { 7 } - 4$