Question

If m(x)=x 5/x-1 and n(x) = x – 3, which function has the same domain as (m*n)(x)

Answer 1

Answer:
m(x) has the same domain as (m*n)(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 (m*n)(x):
(m*n)(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 :)