Question

If a(x) = 3x + 1 and g(x)=1/x-13 , what is the domain of (f*g)(x)?

Answer 1

g(x)=√​4+x​2​​​​​

\displaystyle h\left(x\right)=\frac{4}{3-x}h(x)=​3−x​​4​​

\displaystyle f=h\circ gf=h∘g

Answer 2

For this case, the first thing you should do is multiply both functions.
We have then:
f (x) = 3x + 1
g (x) = 1 / x-13
Multiplying we have:
(f * g) (x) = (3x + 1) * (1 / x-13)
Rewriting the function:
(f * g) (x) = (3x + 1) / (x-13)
Therefore the domain of the function will be:
x that belongs to all reals without including x = 13
Answer:
the domain of (f * g) (x) is:
x that belongs to all reals without including x = 13