Question

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

Answer 1

A,B, and C

Step-by-step explanation

If

`f(g(x))=g(f(x))=x`

then f and g are inverse functions.

A.

`f(x) = (x + 1)/(6)`

`g(x) = 6x - 1`

`f(g(x)) = (6x - 1 + 1)/(6) = (6x)/(6) = x`

B.

`f(x) = (x - 4)/(19)`

`g(x) = 19x + 4`

`f(g(x)) = (19x + 4 - 4)/(19) = (19x)/(19) = x`

C.

`f(x) = {x}^(5)`

`g(x) = \sqrt[5]{x}`

`f(g(x)) = (\sqrt[5]{x})^(5) = x`

D.

`f(x) = (x)/(x + 20 )`

`g(x) = (20x)/(x - 1)`

`f(g(x)) = ( (20x)/(x - 1) )/( (20x)/(x - 1) + 20) = (20x)/(40x - 20) = (x)/(2x - 1)`

The correct answers are A, B , C