3 years ago

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Mathematics

1 answer:

Contact [7]3 years ago

5 0

Answer:

Step-by-step explanation:

gggehheueuru jshgsgsgsgsgsggsgs

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Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

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ANSWER

See below

EXPLANATION

Given

$f(x) = \frac{ {x}- 9 }{x + 5}$

and

$g(x) = \frac{ - 5x - 9}{x - 1}$

$(f \circ \: g)(x)= \frac{ (\frac{ - 5x - 9}{x - 1})- 9 }{(\frac{ - 5x - 9}{x - 1} )+ 5}$

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9(x - 1)}{x - 1}}{\frac{ - 5x - 9 + 5(x - 1)}{x - 1} }$

Expand:

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9x + 9}{x - 1}}{\frac{ - 5x - 9 + 5x - 5}{x - 1} }$

$(f \circ \: g)(x)= \frac{ \frac{ - 5x - 9x + 9 - 9}{x - 1}}{\frac{ - 5x + 5x - 5 - 9}{x - 1} }$

$(f \circ \: g)(x)= \frac{ \frac{ - 14x }{x - 1}}{\frac{ -14}{x - 1} }$

Since the denominators are the same, they will cancel out,

$(f \circ \: g)(x)= \frac{ - 14x}{ - 14} = x$

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