A. Given the functions f and g, the function (f+g)(x)= +. b....

a. Given the functions $f$ and $g,$ the function $(f+g)(x)=$___ +____.
b. Given the functions $f$ and $g$, the function $\left(\frac{f}{g}\right)(x)=\frac{f(x)}{\square},$ provided___$\neq 0$.
c. The function $f$ composed with $g$ is defined by the rule $(f \circ g)(x)=$___.

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Key Concepts

Function Division

Function division involves creating a new function by dividing the output of one function by the output of another, provided that the denominator function is not zero to avoid undefined expressions. The form for division is (f/g)(x) = f(x) / g(x), and careful attention must be given to the domain of the resulting function, ensuring that g(x) ? 0.

Function Composition

Function composition is the operation of applying one function to the result of another. The composite function, expressed as (f ? g)(x) = f(g(x)), indicates that the function g is applied first, and then the function f is applied to the result of g. This creates a new function whose behavior is determined by the sequential application of the original functions.

Function Addition

Function addition is a process in which two functions are combined by adding their individual outputs for any given input. The sum function, defined as (f+g)(x) = f(x) + g(x), creates a new function whose value at each point is the sum of the values of the original functions at that point.

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