Consider the following functions. f(x) = x² and g(x) = √√x +3 Step 2 of 2: Find the formula for (gof)(x) and simplify your answer. Then find the domain for (gof)(x). Round your answer to two decimal places, if necessary. Answer (gof)(x) = Domain= Keypad Keyboard Shortcuts
Consider the following functions. f(x) = x² and g(x) = √√x +3 Step 2 of 2: Find the formula for (gof)(x) and simplify your answer. Then find the domain for (gof)(x). Round your answer to two decimal places, if necessary. Answer (gof)(x) = Domain= Keypad Keyboard Shortcuts
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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![Title: Combining Functions - Example Problem
**Lesson 5.3: Combining Functions**
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**Question 12 of 14, Step 2 of 2**
**Task:** Consider the following functions.
Given:
\[ f(x) = x^2 \]
\[ g(x) = \sqrt{x + 3} \]
**Step 2 of 2:**
- Find the formula for \((g \circ f)(x)\) and simplify your answer.
- Then find the domain for \((g \circ f)(x)\).
- Round your answer to two decimal places, if necessary.
**Answer:**
- Formula: \((g \circ f)(x) = \sqrt{x^2 + 3}\)
- **Domain:**
- The expression under the square root, \(x^2 + 3\), must be greater than or equal to zero for the function to be defined.
- Since \(x^2\) is always non-negative, \(x^2 + 3\) is always positive.
- Thus, the domain of \((g \circ f)(x)\) is all real numbers, \(\mathbb{R}\).
---
This example demonstrates how to work with composite functions and determine their domains based on the function definitions provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58a09e17-7e97-4fdf-b2e2-241ffebdae04%2Ffe5c5c59-94fd-442b-8b97-dfe531975a78%2Fkx49nce_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Combining Functions - Example Problem
**Lesson 5.3: Combining Functions**
---
**Question 12 of 14, Step 2 of 2**
**Task:** Consider the following functions.
Given:
\[ f(x) = x^2 \]
\[ g(x) = \sqrt{x + 3} \]
**Step 2 of 2:**
- Find the formula for \((g \circ f)(x)\) and simplify your answer.
- Then find the domain for \((g \circ f)(x)\).
- Round your answer to two decimal places, if necessary.
**Answer:**
- Formula: \((g \circ f)(x) = \sqrt{x^2 + 3}\)
- **Domain:**
- The expression under the square root, \(x^2 + 3\), must be greater than or equal to zero for the function to be defined.
- Since \(x^2\) is always non-negative, \(x^2 + 3\) is always positive.
- Thus, the domain of \((g \circ f)(x)\) is all real numbers, \(\mathbb{R}\).
---
This example demonstrates how to work with composite functions and determine their domains based on the function definitions provided.
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