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

1 Answer
Antoine
Apr 12, 2015

**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!

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