Question

HELP ASAP ~ WILL GIVE BRAINLIEST ASAP

Answer 1

Answer:

Domain [-5,∞)

Range [0,∞)

Step-by-step explanation:

Part 1) Find the domain

we have

$f(x)=\frac{1}{2}\sqrt{x+5}$

we know that

The radicand must be greater than or equal to zero

so

$x+5\geq 0$

solve for x

subtract 5 both sides

$x\geq -5$

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

$f(x)=\frac{1}{2}\sqrt{x+5}$

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

For x=-5

$f(x)=\frac{1}{2}\sqrt{-5+5}$

$f(x)=0$

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,∞)