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

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

Step-by-step 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.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0