Question

h(x)= 4/x-5 What is the domain of h? A: All real values of x such that x ≠ 4 B:All real values of x such that x ≥ 4 C: All real values of x such that x ≠5 D: All real values of x such that x ≤ 5 E: All real values of x

Answer 1

C. All real values of x such that x ≠ 5

Explanation:

Given

h(x) = 4/(x - 5)

Required

Determine the domain of the function

To get the domain of the function, we start by writing out the denominator in the following format:

x - 5 ≠ 0

Add 5 to both sides

x - 5 + 5 ≠ 0 + 5

x ≠ 5

The domain can be written in builder notation as follows

x = { x ∈ R: x≠ 5}

The above expression implies that the domain of the function is all real values of x but x ≠ 5

From the list of options, the correct answer is C.