# Function Composition Problems### Problem StatementFind the compositions \( h \circ g \) and \( g \circ h \) for the following functions:### Part a1. Given: - \( g(x) = \sqrt[3]{x - 4} \) - \( h(x) = x^3 + 4 \)2. Find: - \( h \circ g \) - \( g \circ h \)### Part b1. Given: - \( g(x) = x^2 + 1 \) - \( h(x) = x + 2 \)2. Find: - \( h \circ g \) - \( g \circ h \)In these problems, students are required to substitute the function \( g(x) \) into the function \( h(x) \) to find \( h \circ g \), and substitute \( h(x) \) into the function \( g(x) \) to find \( g \circ h \). This exercise helps in understanding the concept of function composition which is fundamental in algebra and calculus.

Answered: Find the h °g and g °h for following:…

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Find the h °g and g °h for following: a. If g(x) = Vx – 4 and h(x) = x³ + 4 b. If g(x) = x² + 1 and h(x) = x +2

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

# Function Composition Problems

### Problem Statement
Find the compositions \( h \circ g \) and \( g \circ h \) for the following functions:

### Part a
1. Given:
- \( g(x) = \sqrt[3]{x - 4} \)
- \( h(x) = x^3 + 4 \)

2. Find:
- \( h \circ g \)
- \( g \circ h \)

### Part b
1. Given:
- \( g(x) = x^2 + 1 \)
- \( h(x) = x + 2 \)

2. Find:
- \( h \circ g \)
- \( g \circ h \)

In these problems, students are required to substitute the function \( g(x) \) into the function \( h(x) \) to find \( h \circ g \), and substitute \( h(x) \) into the function \( g(x) \) to find \( g \circ h \). This exercise helps in understanding the concept of function composition which is fundamental in algebra and calculus.

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