Answer:
range of f is [0,3]
Step-by-step explanation:
The "square root" symbol, [tex]\sqrt{\text{ \quad }}[/tex], is a function. Â As a result, it only has a single output because functions must only have a single output for each input.
Thinking about it graphically, if the square root function did give both a positive and a negative result, the function "f" would not pass the vertical line test and it would not be a function.
When solving an equation like [tex]x^2=25[/tex], to solve, we must apply the square root property. Â The square root property says that to find both solutions, one must look at both the positive and the negative of the square root. Â So, to solve:
[tex]x^2=25[/tex]
Apply square root property...
[tex]\sqrt{x^2} = \pm \sqrt{25}[/tex]
[tex]x=\sqrt{25}[/tex]  or  [tex]x=-\sqrt{25}[/tex]
[tex]x=5[/tex]  or  [tex]x=-5[/tex]
In this case, because the square root function itself only outputs non-negative results (so, including zero, as you already identified), the range will only be [0,3].
