Find f+g, f-g, fg, and (f)/(8) . Determine the domain for each function. f(x)=x-5, g(x)=3 x^2

Name: Problem 33, Chapter 1: Precalculus
Uploaded: 2021-08-27T00:10:14-08:00
Duration: 4 min
Channel: Hannah Wilkinson
Description: Find f+g, f-g, fg, and (f)/(8) . Determine the domain for each function. f(x)=x-5, g(x)=3 x^2

Find f+g, f-g, fg, and (f)/(8) . Determine the domain for...

Key Concepts

Domain of Polynomial Functions

The domain of a function is the complete set of possible input values for which the function is defined. In the context of polynomial functions, since there are no inherent restrictions such as division by zero or taking even roots of negative numbers, the domain is typically all real numbers.

Function Addition

This concept involves combining two functions by adding their outputs pointwise. When functions are added, the resultant function has outputs defined by the sum of the outputs of the original functions at each input value.

Function Subtraction

Subtraction of functions is the process of creating a new function by deducting one function's output from another's at each input value. This operation is performed pointwise, meaning the new function's value at any point is determined by subtracting the second function's value from the first's.

Function Multiplication

Multiplying functions involves forming a new function where each output is the product of the outputs of the original functions at the same input. This combines the effects of both functions into a single expression evaluated at every applicable input.

Scalar Multiplication of Functions

Scalar multiplication means multiplying every output of a function by a constant. This operation scales the function's graph, modifying its amplitude while leaving the input domain unchanged.

Transcript

00:01 Hello, for this question we will be looking at domains and function notation to be able to solve the given answer.

00:09 So just as a reminder, domain is for our intents on purposes, the values that x can be for our function.

00:18 Domain restrictions occur when we have a fraction or when we have a square root with a fraction.

00:26 If we have an x in the denominator or the bottom of our fraction, there's the value of x that makes the denominator 0 is a restriction.

00:38 Likewise with square roots, we can't have negative.

00:42 So any value of x that makes a negative number underneath our square root is also a restriction.

00:49 So going through, we have our two functions.

00:52 We're going to go through with several different combinations of the functions.

00:57 And find the domain.

00:59 So first we're going to add them.

01:03 So f plus g of x is equal to x minus 5 plus 3x squared or another would you write that would be 3x squared plus x minus 5.

01:19 Now because there's no fraction and there's no square root, we don't have any restrictions.

01:26 So our domain is going to be everything between negative infinity and positive infinity.

01:35 Now subtracting the two functions, i will have x minus 5 minus 3x squared.

01:44 So rewriting that, our new function, f minus g of x, gives us negative 3x squared plus x minus 5...

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