Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem Statement:**
Given that \( f(x) = 3x + 1 \) and \( h(x) = x^3 \), find \( (h \circ f)(1) \).
**Solution:**
To solve for \( (h \circ f)(1) \), we need to compute the composition of the functions \( h \) and \( f \) at \( x = 1 \).
1. **Find \( f(1) \):**
\[
f(1) = 3(1) + 1 = 3 + 1 = 4
\]
2. **Substitute \( f(1) \) into \( h(x) \):**
\[
h(f(1)) = h(4) = 4^3 = 64
\]
Therefore, \( (h \circ f)(1) = 64 \).
**Final Answer:**
\[
(h \circ f)(1) = \boxed{64}
\]
*(Simplify your answer.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9cbab74a-3ffd-41a5-b168-38fe06f861a5%2F77664582-8ab0-4d68-ad45-5bff4a006c8e%2F7umsxdkc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given that \( f(x) = 3x + 1 \) and \( h(x) = x^3 \), find \( (h \circ f)(1) \).
**Solution:**
To solve for \( (h \circ f)(1) \), we need to compute the composition of the functions \( h \) and \( f \) at \( x = 1 \).
1. **Find \( f(1) \):**
\[
f(1) = 3(1) + 1 = 3 + 1 = 4
\]
2. **Substitute \( f(1) \) into \( h(x) \):**
\[
h(f(1)) = h(4) = 4^3 = 64
\]
Therefore, \( (h \circ f)(1) = 64 \).
**Final Answer:**
\[
(h \circ f)(1) = \boxed{64}
\]
*(Simplify your answer.)*
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