Answer:
Function [tex]f(x)=\sqrt{-x}[/tex] has domain [tex](-\infty ,0][/tex]
Function [tex]f(x)=x^2+4[/tex] has range [tex][4 ,\infty )[/tex]
Step-by-step explanation:
Domain of the function [tex]f(x)[/tex] refers to the values of [tex]x[/tex] and the range refers to the values that the function [tex]f(x)[/tex] takes for various values of [tex]x[/tex].
Consider a function [tex]f(x)=\sqrt{-x}[/tex]
As value within the square root is non-negative.
[tex]-x\geq 0\\x\leq 0[/tex]
So, domain is [tex](-\infty ,0][/tex]
Now, consider a function [tex]f(x)=x^2+4[/tex]
Clearly,
[tex]x^2\geq 0\\x^2+4\geq 4\\f(x)\geq 4[/tex]
So,
range of [tex]f(x)[/tex] is [tex][4 ,\infty )[/tex]
