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what are the domain and range of the function?

f(x)=12x+5√

domain: [−5, ∞)

range: (−∞, ∞)

domain: [0, ∞)

range: (−5, ∞)

domain: (−5, ∞)

range: (0, ∞)

domain: [−5, ∞)

range: [0, ∞)

Domain [-5,∞)

Range [0,∞)

Step-by-step explanation:

Part 1) Find the domain

we have

we know that

The radicand must be greater than or equal to zero

so

solve for x

subtract 5 both sides

The solution for x is the interval [-5,∞)

All real numbers greater than or equal to -5

Remember that

The domain of a function is the set of all possible values of x

therefore

The domain of the function f(x) is the interval  [-5,∞)

Part 2) Find the range

we have

Find the value of f(x) for the minimum value of x

For x=-5

The minimum value of f(x) is equal to zero

so

The solution for f(x) is the interval [0,∞)

All real numbers greater than or equal to 0

Remember that

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

therefore

The range of the function is the interval [0,∞)

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x