Question

How do you find the domain of the function `f(x) = sqrt(4 - x^2)`?

Answer 1

**Answer: ** `-2<= x <= 2`

The domain of any function is the set of values of `x` that can produce a real output `y` or `f(x)`

So you would bear with me that if `4 - x^2` is negative then you have you would have the square root of a negative number which is imaginary and not real

Hence the function returns a real value when `4 - x^2` is positive or zero

That is `4 - x^2 >= 0`

Hence we find the range of value that the above inequality represents,

Here we go,

`4 - x^2 >= 0 => (2 - x)(2 + x)>=0`

`=> -1*(x - 2)(x + 2)>=0`

`=> (x - 2)(x + 2)<=0`

`=> -2<= x <= 2` is the required domain!