Answer
Option D is the pair of functions which is not a pair of inverse function.
Step-by-step explanation
First of, the inverse of a function is a function that reverses the actions of the function. That is, for the inverse function, if we are given f(x), we would be able to obtain x.
The step to finding a function's inverse is to write y instead of f(x). We then rewrite by replacing the y by x and then make y the subject of formula, the y which is a subject of formula now, represents the inverse function, f⁻¹(x).
For each of them, we can get the other one from it.
f(x) = (x + 1)/6
y = (x + 1)/6
x = (y + 1)/6
Cross multiply
6x = y + 1
y = 6x - 1
g(x) = 6x - 1
f(x) = (x - 4)/19
y = (x - 4)/19
x = (y - 4)/19
19x = y - 4
y = 19x + 4
g(x) = 19x + 4
f(x) = x⁵
y = x⁵
x = y⁵
y = 5√x
g(x) = 5√x
Only option D doesn't give the inverse of the other function.
Hope this Helps!!!