Answer:
m(x) has the same domain as (mn)(x)
Explanation:
1- For m(x):
m(x) is a fraction. This means that the denominator cannot be zero, otherwise, the fraction would be undefined.
The denominator of m(x) would be zero at x = 1.
This means that the domain of m(x) can be any real number except 1
2- For n(x):
The value of x in n(x) can be any number. This is because there is no value that would make n(x) undefined.
This means that the domain of n(x) is all real numbers
3- For (mn)(x):
(mn)(x) = m(x) n(x) = \(\frac{x-5}{x-1} *(x-3) = \frac{(x-5)(x-3)}{(x-1)}\)
We can note that the product is also a fraction. This means that the denominator cannot be zero.
The denominator here will be zero at x = 1.
This means that the domain of (m*n)(x) is all real numbers except 1.
This is the same as the domain of m(x)
Hope this helps :)
