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.

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step-by-step explanation:

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2