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Chapter 2: Problem 104

If equations for \(f\) and \(g\) are given, explain how to find \(f-g .\)

Short Answer

Expert verified
To find \(f-g\), define a new function \(h(x)\) where each value of \(h(x)\) equals \(f(x) - g(x)\). This means, subtract the value of the function \(g\) at \(x\) from the value of the function \(f\) at \(x\). Do this for all values of \(x\).

Step by step solution

01

Define the given functions

First, the equations for the functions \(f\) and \(g\) need to be clearly defined. These could be in any form based on the variables they use.
02

Define the subtraction operation

Subtraction of functions is performed by subtracting the output values of one function from the corresponding output values of the other function. In other words, the difference \(f-g\) is a new function \(h\), where for each input \(x\), \(h(x) = f(x) - g(x)\). This means you subtract the value of function \(g\) at \(x\) from the value of function \(f\) at \(x\).
03

Perform the subtraction

Now, perform the subtraction operation for all values of \(x\). Make sure to simplify the results if possible to get a simplified equation for the function \(f-g\).

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Most popular questions from this chapter

Give an example of a relation with the following characteristics: The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ x^{2}+y^{2}=16 $$

Exercises \(98-100\) will help you prepare for the material covered in the first section of the next chapter. In Exercises \(98-99,\) solve each quadratic equation by the method of your choice. $$ -x^{2}-2 x+1=0 $$

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} x^{2}+y^{2} &=16 \\ x-y &=4 \end{aligned} $$

What is a circle? Without using variables, describe how the definition of a circle can be used to obtain a form of its equation.
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