Question

How do you find the domain of `f(x) = sqr(25 - x^2)`?

Answer 1

Domain: [-5, 5]
Range: [0, 5]

Explanation:

The given equation is `f(x)=sqrt(25-x^2)` and any value of x>5 will make the radicand negative. Also any value of x<-5 will make the radicand negative, therefore the domain is `-5<=x<=5`.

The range is found by checking the value of f(x) at `x=+-5` and `x=0`. When `x=+-5` the value of `f(x)=0` and when `x=0`, the value of `f(x)=5`. We can conclude that Range is `0<=f(x)<=5`

God bless....I hope the explanation is useful.