Question

In what interval is the function f(x)=squareroot x^2+5x+4 defined

Answer 1

-4 <= x >= -1

Explanation:

Find where x^2+5x+4 < 0, negative sq roots are imagingary numbers.

So factor

(x + 4) (x + 1) = 0

x = -4 and x = -1

so x must be <= -4 or x >= -1

the interval is

-4 <= x >= -1

Answer 2

9514 1404 393

Answer:

(-∞, -4] U [-1, ∞)

Explanation:

The quadratic expression factors as ...

x^2 +5x +4 = (x +4)(x +1)

The zeros of this expression are where these factors are zero, at x=-4 and x=-1. The product is negative when one factor is negative and the other is positive, in the region -4 < x < -1. It is non-negative elsewhere. f(x) is defined where the quadratic is not negative, on the union of intervals ...

(-∞, -4] U [-1, ∞)