Question

If the final composition of two functions ends up as

1/x−3
What would be the domain restriction? Describe how you found that answer.
a)x≤3
b) x≥3
c) x≠3
d) x>3

Answer 1

The domain restriction for the function 1/(x-3) is x ≠ 3 because the function is undefined when x equals 3, as division by zero cannot occur.

Step-by-step explanation:

The student asked about the domain restriction for the composition of two functions that results in 1/(x-3). To determine the domain of this function, we must identify values of x where the function is undefined. The function 1/(x-3) has a denominator of x-3, which means it cannot equal zero because division by zero is undefined. Consequently, in the case of 1/(x-3), the x value that makes the denominator zero is 3. Therefore, the domain of the function excludes this value, and the domain restriction is x ≠ 3. Thus, the correct answer to the question is option (c) x ≠ 3, meaning x cannot equal 3.