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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
To find the difference of the functions [tex]\( s(x) \)[/tex] and [tex]\( r(x) \)[/tex], we follow these steps:

1. Write down the given functions:
[tex]\[ r(x) = -x^2 + 3x \][/tex]
[tex]\[ s(x) = 2x + 1 \][/tex]

2. Calculate the difference [tex]\( (s - r)(x) \)[/tex]:
[tex]\[ (s - r)(x) = s(x) - r(x) \][/tex]

3. Substitute the expressions for [tex]\( s(x) \)[/tex] and [tex]\( r(x) \)[/tex]:
[tex]\[ s(x) - r(x) = (2x + 1) - (-x^2 + 3x) \][/tex]

4. Simplify the expression:
[tex]\[ (2x + 1) - (-x^2 + 3x) = 2x + 1 + x^2 - 3x \][/tex]

5. Combine like terms:
[tex]\[ 2x + 1 + x^2 - 3x = x^2 + (2x - 3x) + 1 = x^2 - x + 1 \][/tex]

Therefore, the difference of the functions [tex]\( s(x) \)[/tex] and [tex]\( r(x) \)[/tex] is:
[tex]\[ (s - r)(x) = x^2 - x + 1 \][/tex]
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