Question

pleaseFind the domain of f(x)=x+sqroot (25-(x^2))

Answer 1

For the square root to return real values, we need

25-x^2 >= 0
so,
25>=x^2
x^2<=25

So:
-5<=x<=5

Answer 2

thank you

Answer 3

note that:
25-x^2>=0

means that:
(5-x)(5+X)>=0



So, looking at a number line at (5-x) and (5+x) to see when each of them
is positive , negative or zero .
Then looking at their product (5-x)(5+x) ; is how we see that:

25-x^2 >= 0 when -5 <= x <= 5



<------------+-----------------------+--------------->
-5 5
(5-x) + + + + + + + + + + + + + + + + + + + 0 - - - - - - - - - - -

(5+x) - - - - - - 0 + + + + + + + + + + + + + + + + + + + + + + +

(5-x)(5+x) - - - - - - - 0 + + + + + + + + + + + + + 0 - - - - - - - - - - -

Answer 4

oh i see thanks a lot again :)