Question

Can someone help me please

Answer 1

The inverse function of g(x) is:

$f(x) = -\frac{3}{x + 4}$

So the correct option is D.

How to get the inverse of g(x)?

Here we have the function:

$g(x) = -\frac{3}{x} - 4$

Remember that two functions f(x) and g(x) are inverses if:

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

Then we must have:

$g(f(x)) = -\frac{3}{f(x)} - 4 = x$

Solving for f(x), we get:

$-\frac{3}{f(x)} - 4 = x\\\\ \frac{3}{f(x)} +4 = -x$

$\frac{3}{f(x)} = -x - 4\\\\3 = (-x - 4)*f(x)\\\\\frac{3}{-x - 4} = f(x) = -\frac{3}{x + 4}$

Then the correct option is D.

If you want to learn more about inverse functions:

brainly.com/question/14391067

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