Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
Find \( f(f(1)) \) for
\[
f(x) =
\begin{cases}
9 & \text{if } x < 0 \\
9x + 15 & \text{if } 0 < x < 9 \\
x^2 - 4 & \text{if } x \geq 9
\end{cases}
\]
**Solution:**
First, evaluate \( f(1) \):
- Since \( 1 \) is in the interval \( 0 < x < 9 \), we use the function \( f(x) = 9x + 15 \).
\[
f(1) = 9(1) + 15 = 24
\]
Next, evaluate \( f(24) \):
- Since \( 24 \geq 9 \), we use the function \( f(x) = x^2 - 4 \).
\[
f(24) = 24^2 - 4 = 576 - 4 = 572
\]
Thus, \( f(f(1)) = 572 \).
**Answer:**
\[
f(f(1)) = 572
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92ab3c20-a3cd-4c1e-8775-52ac5ed4d4cf%2Ff13444e7-560e-497c-910d-f2bff9da24e7%2Frzr60su_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( f(f(1)) \) for
\[
f(x) =
\begin{cases}
9 & \text{if } x < 0 \\
9x + 15 & \text{if } 0 < x < 9 \\
x^2 - 4 & \text{if } x \geq 9
\end{cases}
\]
**Solution:**
First, evaluate \( f(1) \):
- Since \( 1 \) is in the interval \( 0 < x < 9 \), we use the function \( f(x) = 9x + 15 \).
\[
f(1) = 9(1) + 15 = 24
\]
Next, evaluate \( f(24) \):
- Since \( 24 \geq 9 \), we use the function \( f(x) = x^2 - 4 \).
\[
f(24) = 24^2 - 4 = 576 - 4 = 572
\]
Thus, \( f(f(1)) = 572 \).
**Answer:**
\[
f(f(1)) = 572
\]
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