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vova2212 [387]
3 years ago
6

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

Mathematics
1 answer:
Artemon [7]3 years ago
6 0

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

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