Add and subtract functions

Learning Objectives Define the sum and difference of two functions using standard notation. Algebraically compute the sum of two functions, (f+g)(x), given the expressions for f(x) and g(x). Algebraically compute the difference of two functions, (f-g)(x), given the expressions for f(x) and g(x). Evaluate the sum or difference of two functions at a specific numerical input, such as (f-g)(3). Determine the domain of a new function created by the addition or subtraction of two functions. Interpret the sum or difference of functions from their graphs at a given point. Model a real-world scenario by combining two functions through addition or subtraction. A company's revenue is modeled by one function and its costs by another. How can we create a single function to model i...

TermDefinitionExample FunctionA mathematical rule that assigns exactly one output value for each unique input value.f(x) = 2x + 3. If the input is x=4, the unique output is f(4) = 2(4) + 3 = 11. Domain of a FunctionThe complete set of all possible input values (x-values) for which the function is defined.For the function f(x) = √x, the domain is [0, ∞) because we cannot take the square root of a negative number in the real number system. Sum of FunctionsA new function, denoted (f+g)(x), created by adding the outputs of two functions, f(x) and g(x), for the same input x.If f(x) = x² and g(x) = 5x, then (f+g)(x) = x² + 5x. Difference of FunctionsA new function, denoted (f-g)(x), created by subtracting the outputs of g(x) from f(x) for the same input x.If f(x) = 10x and g(x) = 3x - 1, then (...

Sum of Functions Formula (f+g)(x) = f(x) + g(x) To find the sum of two functions, add their expressions together and simplify by combining like terms. Difference of Functions Formula (f-g)(x) = f(x) - g(x) To find the difference of two functions, subtract the entire expression of the second function from the first. Be sure to distribute the negative sign to all terms of the second function. Domain of Sums and Differences Domain(f+g) = Domain(f) ∩ Domain(g) The domain of the function resulting from adding or subtracting f(x) and g(x) is the intersection of their individual domains. In other words, an x-value must be valid for both f(x) and g(x) to be in the domain of their sum or difference.