Question

Over which interval of the domain is function h decreasing?

hx= beginarrayl 2x,x<1 square root of x+3,x ≥ q 1endarray
A. (1,00)
B. ([infinity], [infinity])
C. (-00, 1)
D. The function is increasing only.

Answer 1

The function h(x) is increasing over its entire domain.

Step-by-step explanation:

The function h(x) is defined as:

• h(x) = 2x, if x < 1
• h(x) = √(x + 3), if x ≥ 1

To determine over which interval the function h(x) is decreasing, we need to find the intervals where the derivative of the function is negative. Taking the derivative of each part of the function:

• For x < 1, the derivative of h(x) = 2x is h'(x) = 2
• For x ≥ 1, the derivative of h(x) = √(x + 3) is h'(x) = 1/(2√(x + 3))

We can see that the derivative is always positive for both parts of the function, which means that the function h(x) is increasing over its entire domain. Therefore, the correct option is D) The function is increasing only.