If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?

Question:

If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?

h (x) = StartFraction x + 5 Over 11 EndFraction

h (x) = StartFraction 11 Over x minus 1 EndFraction

h (x) = StartFraction 11 Over x minus 4 EndFraction

h (x) = StartFraction 11 Over x minus 3 EndFraction

Option C: has the same domain as

Explanation:

It is given that and

Let us find the domain of

Now, let us equate the denominator equal to zero to determine the domain.

Thus, the function becomes undefined at the point

Hence, the domain of is

Now, we shall find the function which has the same domain as

Option A:

The function h(x) has the domain of set of all real numbers

Thus, the interval is not the same domain as

Hence, Option A is not the correct answer.

Option B:

Equating the denominator equal to zero, the function becomes undefined at the point

Thus, the function h(x) has the domain of is not the same domain as

Hence, Option B is not the correct answer.

Option C:

Equating the denominator equal to zero, the function becomes undefined at the point

Thus, the function h(x) has the domain of is the same domain as

Hence, Option C is the correct answer.

Option D:

Equating the denominator equal to zero, the function becomes undefined at the point

Thus, the function h(x) has the domain of is not the same domain as

Hence, Option D is not the correct answer.

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step-by-step explanation: