Question

find the difference of functions s and r shown below.\\( r(x) = -x^2 + 3x \\) \\( s(x) = 2x + 1 \\) \\( (s - r)(x) = \\) \\( \boldsymbol{\text{done}} \\)

Explanation:

Step1: Recall the formula for the difference of functions

The difference of two functions \((s - r)(x)\) is defined as \(s(x)-r(x)\).

Step2: Substitute the given functions

We know that \(s(x) = 2x + 1\) and \(r(x)=-x^{2}+3x\). So, we substitute these into the formula:
\((s - r)(x)=s(x)-r(x)=(2x + 1)-(-x^{2}+3x)\)

Step3: Simplify the expression

First, distribute the negative sign to the terms inside the parentheses:
\((2x + 1)-(-x^{2}+3x)=2x + 1+x^{2}-3x\)
Then, combine like terms. The like terms for \(x\) are \(2x\) and \(-3x\):
\(2x-3x=-x\), so the simplified expression is \(x^{2}-x + 1\)

Answer:

\(x^{2}-x + 1\)