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Subtract Functions

Find the difference of functions [tex]\( s \)[/tex] and [tex]\( r \)[/tex] shown below.

[tex]\[
\begin{array}{l}
r(x) = -x^2 + 3x \\
s(x) = 2x + 1 \\
(s - r)(x) =
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, I can help you find the difference between the functions [tex]\( s(x) \)[/tex] and [tex]\( r(x) \)[/tex]. The functions are given as follows:

[tex]\[ r(x) = -x^2 + 3x \][/tex]
[tex]\[ s(x) = 2x + 1 \][/tex]

We need to find [tex]\( (s - r)(x) \)[/tex], which means we are looking for the function [tex]\( s(x) \)[/tex] minus the function [tex]\( r(x) \)[/tex]. Let's perform the subtraction step-by-step.

1. Start by writing the expression for [tex]\( (s - r)(x) \)[/tex]:

[tex]\[ (s - r)(x) = s(x) - r(x) \][/tex]

2. Substitute the given expressions for [tex]\( s(x) \)[/tex] and [tex]\( r(x) \)[/tex]:

[tex]\[ (s - r)(x) = (2x + 1) - (-x^2 + 3x) \][/tex]

3. Distribute the negative sign across the terms in [tex]\( r(x) \)[/tex]:

[tex]\[ (s - r)(x) = 2x + 1 + x^2 - 3x \][/tex]

4. Combine like terms to simplify the expression:

[tex]\[ (s - r)(x) = x^2 + 2x - 3x + 1 \][/tex]

5. Combine the [tex]\( x \)[/tex] terms:

[tex]\[ (s - r)(x) = x^2 - x + 1 \][/tex]

Therefore, the difference between the functions [tex]\( s(x) \)[/tex] and [tex]\( r(x) \)[/tex] is:

[tex]\[ (s - r)(x) = x^2 - x + 1 \][/tex]

This is the simplified form of the difference of the given functions.
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