Answer:
Domain [-5,∞)
Range [0,∞)
Step-by-step explanation:
Part 1) Find the domain
we have
[tex]f(x)=\frac{1}{2}\sqrt{x+5}[/tex]
we know that
The radicand must be greater than or equal to zero
so
[tex]x+5\geq 0[/tex]
solve for x
subtract 5 both sides
[tex]x\geq -5[/tex]
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
[tex]f(x)=\frac{1}{2}\sqrt{x+5}[/tex]
Find the value of f(x) for the minimum value of x
For x=-5
[tex]f(x)=\frac{1}{2}\sqrt{-5+5}[/tex]
[tex]f(x)=0[/tex]
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,∞)
