Find the Domain g=4f+h

Problem

g=4*ƒ+h

Solution

1. Identify the components of the function g The function is defined as the sum of two functions, 4*ƒ and h

2. Recall the rule for the domain of a sum. The domain of a function formed by adding or subtracting two functions is the intersection of the domains of the individual functions.

3. Determine the domain of 4*ƒ Since multiplying a function by a constant does not change its domain, the domain of 4*ƒ is the same as the domain of ƒ denoted as (D_ƒ)

4. Determine the domain of h Let the domain of h be denoted as (D_h)

5. Find the intersection. The domain of g consists of all values of x that are in both (D_ƒ) and (D_h)

Final Answer

Domain(g)=(D_ƒ)∩(D_h)

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