Lewis Hamilton
09/14/2024 · Middle School
Evaluate the function \( f(x)=x^{2}+9 x-2 \) at the given values of the independent variable and simplify. \( \begin{array}{lll}\text { a. } f(9) & \text { b. } f(x+8) & \text { c. } f(-x)\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Substitute \( x=9 \) into the expression \( x^{2}+9x-2 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(x^{2}+9x-2\)
- step1: Substitute:
\(9^{2}+9\times 9-2\)
- step2: Multiply the numbers:
\(9^{2}+81-2\)
- step3: Evaluate the power:
\(81+81-2\)
- step4: Calculate:
\(160\)
Substitute \( x=x+8 \) into the expression \( x^{2}+9x-2 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(x^{2}+9x-2\)
- step1: Substitute:
\(\left(x+8\right)^{2}+9\left(x+8\right)-2\)
- step2: Expand the expression:
\(x^{2}+16x+64+9\left(x+8\right)-2\)
- step3: Expand the expression:
\(x^{2}+16x+64+9x+72-2\)
- step4: Add the terms:
\(x^{2}+25x+134\)
Substitute \( x=-x \) into the expression \( x^{2}+9x-2 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(x^{2}+9x-2\)
- step1: Substitute:
\(\left(-x\right)^{2}+9\left(-x\right)-2\)
- step2: Multiply the numbers:
\(\left(-x\right)^{2}-9x-2\)
- step3: Rewrite the expression:
\(x^{2}-9x-2\)
a. \( f(9) = 160 \)
b. \( f(x+8) = x^{2}+25x+134 \)
c. \( f(-x) = x^{2}-9x-2 \)
Quick Answer
a. \( f(9) = 160 \)
b. \( f(x+8) = x^{2}+25x+134 \)
c. \( f(-x) = x^{2}-9x-2 \)
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