Problem 104 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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 \(x\).

Step 3: 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 \(f-g\).