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
Answer:
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.