Answered

IDNLearn.com offers a comprehensive platform for finding and sharing knowledge. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.

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

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

Sagot :

GinnyAnsweridn
To find the difference between the functions [tex]\( s(x) \)[/tex] and [tex]\( r(x) \)[/tex], we need to compute [tex]\( (s - r)(x) \)[/tex]. Here are the detailed steps:

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

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

4. Simplify the expression by distributing and combining like terms:
[tex]\[ (s - r)(x) = 2x + 1 + x^2 - 3x \][/tex]
[tex]\[ (s - r)(x) = x^2 + 2x - 3x + 1 \][/tex]
[tex]\[ (s - r)(x) = x^2 - x + 1 \][/tex]

Therefore, the difference [tex]\( (s - r)(x) \)[/tex] is:
[tex]\[ (s - r)(x) = x^2 - x + 1 \][/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.