Question

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

Answer 1

ANSWER

A,B, and C

EXPLANATION

If

$f(g(x))=g(f(x))=x$

then f and g are inverse functions.

A.

$f(x) = \frac{x + 1}{6}$

$g(x) = 6x - 1$

$f(g(x)) = \frac{6x - 1 + 1}{6} = \frac{6x}{6} = x$

B.

$f(x) = \frac{x - 4}{19}$

$g(x) = 19x + 4$

$f(g(x)) = \frac{19x + 4 - 4}{19} = \frac{19x}{19} = x$

C.

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

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

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

D.

$f(x) = \frac{x}{x + 20 }$

$g(x) = \frac{20x}{x - 1}$

$f(g(x)) = \frac{ \frac{20x}{x - 1} }{ \frac{20x}{x - 1} + 20} = \frac{20x}{40x - 20} = \frac{x}{2x - 1}$

The correct answers are A, B , C