Question

f(x) = √(x + 1) g(x) = √(2 - x) Functions ƒ and g are defined as shown above_ What is the domain of the function f + g ? (A) x >= 0 (B) x >= 1 (C) x >= 2 (D) - 1 <= x <= 2 (E) - 2 <= x <= 1

Answer 1

The domain of the function (f+g), where f(x) = √(x + 1) and g(x) = √(2 - x), is -1 <= x <= 2. This is because the domain of a function resulting from the addition of two functions is the intersection of the domains of the original functions.

Step-by-step explanation:

The domain of a function refers to the set of input or argument values for which the function is defined. For the function f(x) = √(x + 1), the domain is any value of x > = -1 because the radicand (the number under the square root) must be positive or zero. On the other hand, for the function g(x) = √(2 - x), the domain is any value of x <= 2.

When we add two functions to get a new function (f+g), the domain of the result is the intersection of the domains of the two original functions. Therefore, for the function (f + g), the domain is the set of all x such that -1 <= x <= 2. So, the answer is (D) -1 <= x <= 2.

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