Find the functions f+g . f-g . f g and f / g f(x) (1)/(x^2+1) ; g(x)=(1)/(x^2-1)

Name: Problem 22, Chapter 2: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-06-29T14:05:07-08:00
Duration: 2 min 59 s
Channel: Manisha Sarker
Description: Find the functions f+g . f-g . f g and f / g f(x) (1)/(x^2+1) ; g(x)=(1)/(x^2-1)

step 1 In this problem, we have been given two functions, F of X and G of X. Now, first of all, we need

Find the functions f+g . f-g . f g and f / g f(x)...

Key Concepts

Function Addition

Function addition involves combining two functions by adding their respective outputs for each input. This operation creates a new function where each value is the sum of the values produced by the original functions. It is a fundamental arithmetic operation in algebra and calculus that enables the study of combined effects of functions.

Function Subtraction

Function subtraction is the process of combining two functions by subtracting the output of one from the output of the other for each input. This operation results in a new function that represents the difference between the two original functions, and it is useful in problems where one needs to analyze the net effect or variation between mathematical relationships.

Function Division

Function division is about forming a new function by dividing the output of one function by the output of another for each input, symbolically expressed as (f/g)(x) = f(x)/g(x). This operation is critical for handling ratios and rates, and it also introduces important considerations regarding the domain, particularly the restriction of inputs that would make the divisor function zero.

Rational Functions

Rational functions are defined as the ratio of two polynomials and are a common type of function encountered in algebra. They exhibit unique properties such as asymptotes, holes, and specific domains due to the restrictions imposed by their denominators. Understanding rational functions is essential when performing operations like addition, subtraction, multiplication, and division on functions that are expressed in fractional form.

Function Multiplication

Function multiplication involves creating a new function wherein each output is the product of the outputs of two given functions at the same input. This operation is key in understanding interactions between varying quantities, and it is widely used in both algebraic manipulation and more advanced areas like functional analysis.

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