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ryzh [129]
3 years ago
15

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

Mathematics
1 answer:
Tatiana [17]3 years ago
8 0
<span><u><em>Answer:</em></u>
m(x) has the same domain as (m*n)(x)

<u><em>Explanation:</em></u>
<u>1- For m(x):</u>
m(x) is a fraction. This means that the <u>denominator cannot be zero</u>, otherwise, the fraction would be undefined.
The denominator of m(x) would be zero at x = 1.
This means that the <u>domain of m(x) can be any real number except 1</u>

<u>2- For n(x):</u>
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 <u>domain of n(x) is all real numbers</u>

<u>3- For (m*n)(x):</u>
(m*n)(x) = m(x) * n(x) = </span>\frac{x-5}{x-1} *(x-3) =  \frac{(x-5)(x-3)}{(x-1)}
<span>
We can note that the product is also a fraction. This means that the <u>denominator cannot be zero</u>.
The denominator here will be zero at x = 1.
This means that the <u>domain of (m*n)(x) is all real numbers except 1</u>.
<u>This is the same as the domain of m(x)</u>

Hope this helps :)</span>
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