Question

Please help!

Which pair of functions is not a pair of inverse functions?

A. f(x)= x+1/6 and g(x)= 6x-1

B. f(x)= x-4/19 and g(x)= 19x+4

C. f(x)= x5 and g(x)= 5√x

D. f(x)= x/x + 20 and g(x)= 20x/x-1
Thank you!

Answer 1

D. f(x)= x/x + 20 and g(x)= 20x/x-1

Answer 2

Option in D is not an inverse function.

Explanation:

A. Say,
`y = f(x) = (x + 1)/(6)`

⇒ 6y = x + 1

⇒ x = 6y - 1

Here, g(x) = 6x - 1, if g(x) is the inverse function of f(x).

B. Let us assume,
`y = f(x) = (x - 4)/(19)`

⇒ 19y = x - 4

⇒ x = 19x + 4

If g(x) is the inverse function of f(x), then, g(x) = 19x + 4

C. Let
`y = f(x) = x^(5)`

⇒
`x = \sqrt[5]{y}`

Here,
`g(x) = \sqrt[5]{x}`, if g(x) is the inverse function of f(x).

D. Let
`y = f(x) = (x)/(x + 20)`

⇒ yx + 20y = x

⇒ x(y - 1) = - 20y

⇒
`x = (- 20y)/(y - 1)`

Now, if g(x) is the inverse function of f(x), then,
`g(x) = (- 20x)/(x - 1)`

Therefore, option in D is not an inverse function. (Answer)