Please I need urgent help with these question.

Question

1. Find the domain of the function using interval notation.

f(x) = (√x – 6) /  (√ x – 4)

2. sketch the graph of a piecewise function. Write the domain in interval notation.

3.The cost in dollars of making x items is given by the function C(x) = 10x + 500.

a.The fixed cost is determined when the zero items are produced. Find the fixed cost for this item.

b.What is the cost of making 25 items?

c.Suppose the maximum cost allowed is $1500.What are the domain and range of the cost function, C(x)?.

Answer 1

1. The domain is our input, or x-value, possibilities. Looking at our function, we can't have a negative value under the radical sign, and our denominator can't equal 0.

x - 6 ≥ 0

x ≥ 6

x - 4 ≥ 0

x ≥ 4

√(x - 4) ≠ 0

x - 4 ≠ 0

x ≠ 4

Alright, so our value has to be greater than 4 and greater than or equal to 6. We can't use 5, because 5 - 6 = -1 and we can't take the square root of -1, so...

x ≥ 6

2. Yeah, this is on you. Draw a function, any function, and put down the bounds of your x-values.

3. Buddy, find some help, fast.

a. C(0) = 10(0) + 500 = 500

b. C(25) = 10(25) + 500 = your answer

c. 10x + 500 ≤ 1500

10x ≤ 1000

x ≤ 100

The range is your output possibilities.

500 ≥ y ≤ 1500