Answer:
Option D is correct .
Step by step explanation:
A function is given to us and we need to find its inverse . The function is g(x) = -2x⁵ - 2.
So for finding its inverse , exachange x with y .
⇒ g(x) = -2x⁵ - 2 .
Let g(x) = y ,
⇒ y = -2x⁵ - 2 .
Replace x with y ,
⇒ x = -2y⁵ - 2
⇒ x + 2 = -2y⁵
⇒ y⁵ = x+2 / -2
⇒ y⁵ = (-1) ( x + 2) / (-1)(-2)
⇒ y⁵ = -x - 2/ 2
⇒ y = ⁵√ [ ( -x -2)/2 ]
Hence the inverse of the function is ,
[tex]\boxed{\red{\bf f^{-1}(x)=\sqrt[5]{\dfrac{-x-2}{2}}}}[/tex]
Hence the correct option is (D) .
