ANSWER
A,B, and C
EXPLANATION
If
[tex]f(g(x))=g(f(x))=x[/tex]
then f and g are inverse functions.
A.
[tex]f(x) = \frac{x + 1}{6} [/tex]
[tex]g(x) = 6x - 1[/tex]
[tex]f(g(x)) = \frac{6x - 1 + 1}{6} = \frac{6x}{6} = x[/tex]
B.
[tex]f(x) = \frac{x - 4}{19} [/tex]
[tex]g(x) = 19x + 4[/tex]
[tex]f(g(x)) = \frac{19x + 4 - 4}{19} = \frac{19x}{19} = x[/tex]
C.
[tex]f(x) = {x}^{5} [/tex]
[tex]g(x) = \sqrt[5]{x} [/tex]
[tex]f(g(x)) = (\sqrt[5]{x})^{5} = x[/tex]
D.
[tex]f(x) = \frac{x}{x + 20 } [/tex]
[tex]g(x) = \frac{20x}{x - 1} [/tex]
[tex]f(g(x)) = \frac{ \frac{20x}{x - 1} }{ \frac{20x}{x - 1} + 20} = \frac{20x}{40x - 20} = \frac{x}{2x - 1} [/tex]
The correct answers are A, B , C
