Question

In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = √(x + 7), g(x) = √(x - 2)

Accepted Answer

Step 1: Understand the problem. You are tasked with finding the sum (f + g), difference (f - g), product (fg), and quotient (f/g) of the functions f(x) = √(x + 7) and g(x) = √(x - 2). Additionally, you need to determine the domain for each resulting function. Step 2: To find f + g, add the two functions: (f + g)(x) = √(x + 7) + √(x - 2). The domain of this function is determined by the intersection of the domains of f(x) and g(x). For f(x), the domain is x ≥ -7 (since the square root requires non-negative values). For g(x), the domain is x ≥ 2. The intersection of these domains is x ≥ 2. Step 3: To find f - g, subtract the two functions: (f - g)(x) = √(x + 7) - √(x - 2). The domain is the same as for f + g, which is x ≥ 2, because the square root functions must remain defined. Step 4: To find fg, multiply the two functions: (fg)(x) = √(x + 7) * √(x - 2). The domain is again the intersection of the domains of f(x) and g(x), which is x ≥ 2. Step 5: To find f/g, divide the two functions: (f/g)(x) = √(x + 7) / √(x - 2). In addition to the domain restrictions from f(x) and g(x), you must exclude any x-values that make the denominator zero. Since g(x) = √(x - 2), the denominator is zero when x = 2. Therefore, the domain of f/g is x \u003e 2.

In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = √(x + 7), g(x) = √(x - 2)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Function Operations

Domain of a Function

Composite Functions