Find (f+g)(x),(f-g)(x),(f ·g)(x), and ((f)/(g)) for each f(x) and g(x) f(x) =x+5 g(x) =

step 1 F plus G of X is taking the two functions that we have and just adding them together and simplif

Find (f+g)(x),(f-g)(x),(f ·g)(x), and ((f)/(g)) for each...

Key Concepts

Multiplication of Functions

Multiplying functions is achieved by taking the product of the outputs from the individual functions for each input. The new function, (f · g)(x) = f(x) * g(x), provides a combined measure that is sensitive to the scales of both functions.

Subtraction of Functions

Subtracting functions is similar to addition, but involves taking the difference of the outputs. The new function is defined by (f-g)(x) = f(x) - g(x). This represents the net effect when one function's output is decreased by the other’s output at each point in the domain.

Division of Functions

Dividing functions involves forming a new function by dividing the outputs of one function by the outputs of another, expressed as (f/g)(x) = f(x)/g(x). Special attention is required for the domain, as values that make the denominator zero must be excluded to avoid undefined expressions.

Function Operations

This concept refers to performing arithmetic operations such as addition, subtraction, multiplication, and division on functions. These operations are carried out by applying the arithmetic operation to the outputs of the functions for each input, resulting in new functions that describe the combined effect.

Addition of Functions

Adding functions involves creating a new function where each output is the sum of the outputs of the original functions. The expression (f+g)(x) = f(x) + g(x) is computed term by term for each x in the domain, reflecting the cumulative effect.

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