Tucker Cruz
05/02/2024 · Middle School
The functions \( r \) and \( s \) are defined as follows. \[ \begin{array}{l}r(x)=-x+2 \\ s(x)=-2 x^{2}+2 \\ s(r(5))=\square\end{array} \] Find the value of \( s(r(5)) \) \( \times \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the value of \( s(r(5)) \), we first need to calculate \( r(5) \) using the function \( r(x) = -x + 2 \).
Calculating \( r(5) \):
\[
r(5) = -5 + 2 = -3
\]
Next, we need to evaluate \( s(r(5)) \), which is \( s(-3) \). The function \( s(x) \) is defined as \( s(x) = -2x^2 + 2 \).
Now, we calculate \( s(-3) \):
\[
s(-3) = -2(-3)^2 + 2
\]
Calculating \( (-3)^2 \):
\[
(-3)^2 = 9
\]
Now substituting back into the equation:
\[
s(-3) = -2(9) + 2 = -18 + 2 = -16
\]
Thus, the value of \( s(r(5)) \) is:
\[
\boxed{-16}
\]
Quick Answer
\( s(r(5)) = -16 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit