For this case we have the following fusions:
[tex]a (x) = 3x + 1\\b (x) = \frac {1} {x} -4[/tex]
We must find [tex](a * b) (x):[/tex]
By definition:
[tex](a * b) (x) = a (x) * b (x)\\(a * b) (x) = (3x + 1) * (\frac {1} {x} -4)\\(a * b) (x) = \frac {3x} {x} -12x + \frac {1} {x} -4\\(a * b) (x) = 3-12x + \frac {1} {x} -4\\(a * b) (x) = - 12x + \frac {1} {x} -1[/tex]
The domain of the function will be given by all the values for which the function is defined, that is, all real numbers except zero.
Answer:
(-∞, 0) U (0,∞)
