Question

If a(x) = 3x + 1 and 5(x)=1/x-4, what is the domain of (ba)(x)?

Answer 1

For this case we have the following fusions:

$a (x) = 3x + 1\\b (x) = \frac {1} {x} -4$

We must find $(a * b) (x):$

By definition:

$(a * b) (x) = a (x) * b (x)\\(a * b) (x) = (3x + 1) * (\frac {1} {x} -4)\\(a * b) (x) = \frac {3x} {x} -12x + \frac {1} {x} -4\\(a * b) (x) = 3-12x + \frac {1} {x} -4\\(a * b) (x) = - 12x + \frac {1} {x} -1$

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,∞)