Question

How do you find the domain and range of `f(x)= sqrt( x^2+4)`?

Answer 1

Domain: All Real Numbers ℝ
Range: [2,∞)

Explanation:

`x` is squared, so any negative x-values will result in a positive value for `x^2`. The domain is not restricted for x = a positive number or x = 0 since the expression under the radical will always be positive.
Therefore, the domain is all real numbers.

For the range, `x^2` takes its minimum at `x = 0`, so plugging in `x = 0` gives `y = sqrt(x^2+4)=sqrt(0+4)=2` therefore making the range [2,∞).