Question

MARKING AS BRAINLIEST!!

Answer 1

Answer: They are inverses of each other

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Explanation:

We need to check two things:

• f(g(x)) = x
• g(f(x)) = x

If both of those equations are true, then f and g are inverses of each other.

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Part 1

$f(x) = -3x-12\\\\f(g(x)) = -3( g(x) )-12\\\\f(g(x)) = -3\left( \frac{-12-x}{3} \right)-12\\\\f(g(x)) = 12+x-12\\\\f(g(x)) = x$

So far, so good. Now we need to check the other equation mentioned.

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Part 2

$g(x) = \frac{-12-x}{3}\\\\g(f(x)) = \frac{-12-( f(x) )}{3}\\\\g(f(x)) = \frac{-12-( -3x-12 )}{3}\\\\g(f(x)) = \frac{-12+3x+12}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x$

That works out as well. Both equations mentioned are true, which confirms the two original functions are inverses of one another.