Find (f+g)(x) and (f+g) Let f(x)=-4 x and g(x)=-3 x+5 . Find (f+g)(x) (f-g)(x), (f g)(x), an

step 1 If we have two functions, F and G, we can add to track, multiply, and divide the functions. So t

Find (f+g)(x) and (f+g) Let f(x)=-4 x and g(x)=-3 x+5 . Find...

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Key Concepts

Function Addition

Function addition involves creating a new function by adding the outputs of two functions for the same input value. The process is performed pointwise; that is, for any input x, the sum is computed as (f+g)(x) = f(x) + g(x). It is used to combine the effects or contributions of two functions into one unified expression.

Function Subtraction

Function subtraction is analogous to addition but involves finding the difference between two functions at each input value. Specifically, for any x, (f-g)(x) = f(x) - g(x) is computed. This operation is useful when comparing or eliminating effects represented by two separate functional expressions.

Function Multiplication

Function multiplication refers to the pointwise multiplication of two functions, meaning for each input x the new function is defined as (fg)(x) = f(x) * g(x). This operation is utilized in various contexts, such as scaling one function by another or when analyzing combined behaviors of two variables.

Function Division

Function division involves dividing the outputs of two functions for each input value to form a new function defined as (f/g)(x) = f(x) / g(x), provided the denominator g(x) is not zero. This operation is crucial in understanding relationships that require a ratio or rate, while also considering domain restrictions to avoid division by zero.

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