Question

The functions f(x)=√x-3 and g(x)=√x+2 are combined using addition to get function h. Which represents the

combined function?
A h(x)=√x-3+√√x+2₁X≥-3
B h(x)=√x-3+√x+2₁x2-2
C h(x)=√x-3+√√x+2₁x≥2
D h(x)=√x-3+√√x+2₁x≥3

Answer 1

`\textsf{D. }h(x)=√(x-3)+√(x+2),\ x\ge3`

Explanation:

You want h(x) = f(x) +g(x), where f(x) = √(x-3) and g(x) = √(x+2).

Sum

The sum is straightforward:

h(x) = f(x) +g(x)

h(x) = √(x -3) +√(x +2)

Domain

The domain of each function is the set of x-values for which the function is defined. Each square root is undefined for negative values, so the respective domains are ...

• f(x): x ≥ 3
• g(x): x ≥ -2

The domain of h(x) will be the set of values of x that reside in the domains of both f(x) and g(x): x ≥ 3.

Combined function

The combined function is then ...

h(x) = √(x -3) +√(x +2), x ≥ 3 . . . . . . . choice D

<95141404393>