Question

Please help with this difficult one...

Answer 1

The composite function is given as follows:

$(f \circ g)(x) = \frac{2x + 6}{3x + 22}$

The domain of the composite function is: $\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}$

What is the composite function of f(x) and g(x)?

The composite function is given by:

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

In this problem, the functions are:

• $f(x) = \frac{2}{x + 3}$.

• $g(x) = \frac{13}{x + 3}$.

Hence the composite function is:

$(f \circ g)(x) = f\left(\frac{13}{x + 3}\right) = \frac{2}{\frac{13}{x + 3} + 3} = \frac{2(x + 3)}{13 + 3(x + 3)} = \frac{2x + 6}{3x + 22}$

For the domain, we have to remove the points outside the domain of both the primitive and the composite functions, that is, the zeroes of the denominators, hence:

$x + 3 \neq 0 \rightarrow x \neq 3$

$3x + 22 \neq 0 \rightarrow x \neq -\frac{22}{3}$

Hence the domain is:

$\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}$

More can be learned about composite functions at https://brainly.com/question/13502804

#SPJ1