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

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

g (x) = √ 4 + x 2

/displaystyle h/left (x/right) = / frac{4}{3-x} h (x) = 3-x 4

/displaystyle f=h/circ g f=h∘ g