Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, f, circle, g, right parenthesis, left parenthesis, minus, 3, right parenthesis, .(f∘g)(−3).
f, of, x, equals, 2, x, squared, minus, 4, x, plus, 7
f(x)=
2x 
2
 −4x+7
g, of, x, equals, minus, 4, x, minus, 15
g(x)=
−4x−15
Answer
Attempt 2 out of 2

Submit Answer
Still Stuck?
Copyright ©2024 DeltaMath.com All Rights Reserved.Privacy Policy | Terms of Service


To solve \((f \circ g)(-3)\), we need to first understand that \((f \circ g)(x)\) means \(f(g(x))\), meaning we substitute \(g(x)\) into \(f(x)\).

### Step 1: Find \(g(-3)\)
The function \(g(x)\) is given as:
\[
g(x) = -4x - 15
\]
Substitute \(x = -3\) into \(g(x)\):
\[
g(-3) = -4(-3) - 15 = 12 - 15 = -3
\]

### Step 2: Find \(f(g(-3)) = f(-3)\)
Now, use \(g(-3) = -3\) and substitute \(-3\) into the function \(f(x)\). The function \(f(x)\) is given as:
\[
f(x) = 2x^2 - 4x + 7
\]
Substitute \(x = -3\) into \(f(x)\):
\[
f(-3) = 2(-3)^2 - 4(-3) + 7 = 2(9) + 12 + 7 = 18 + 12 + 7 = 37
\]

### Final Answer:
\[
(f \circ g)(-3) = 37
\]

Would you like more details on how function composition works or have any other questions?

Here are five related questions for further practice:
1. Find \((f \circ g)(2)\) using the same \(f(x)\) and \(g(x)\).
2. If \(f(x) = 3x^2 - x + 5\) and \(g(x) = 2x - 1\), find \((f \circ g)(1)\).
3. What is \((g \circ f)(-3)\) using the same functions \(f(x)\) and \(g(x)\)?
4. Find the inverse function of \(g(x) = -4x - 15\).
5. What is the domain of \((f \circ g)(x)\)?

**Tip:** In function composition, always start by evaluating the innermost function before applying the outer function.

Given the definitions of f(x) = 2x^2 - 4x + 7 and g(x) = -4x - 15, find the value of (f ∘ g)(-3).

Learn how to solve the function composition (f ∘ g)(-3) using quadratic and linear functions. This step-by-step guide covers key algebraic concepts and is suitable for students in Grades 9-11. Explore the process of function evaluation, including substitution and simplification.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation