If 
f(x)=x 
2
 +8x−1, 
g(x)=−4x+3, and 
h(x)=7−3x, find 
( 
h
g
​
 )(2).

To solve \((hg)(2)\), we start by finding \(g(2)\) and then use that result to find \(h(g(2))\).

### Given functions:
- \( f(x) = x^2 + 8x - 1 \) 
- \( g(x) = -4x + 3 \)
- \( h(x) = 7 - 3x \)

### Step 1: Find \( g(2) \)
\[
g(x) = -4x + 3
\]
Substituting \(x = 2\):
\[
g(2) = -4(2) + 3 = -8 + 3 = -5
\]

### Step 2: Find \(h(g(2)) = h(-5)\)
\[
h(x) = 7 - 3x
\]
Substituting \(x = -5\):
\[
h(-5) = 7 - 3(-5) = 7 + 15 = 22
\]

Therefore, \((hg)(2) = 22\).

### Final Answer
\[
(hg)(2) = 22
\]

Would you like further details or explanations?

### Related Questions:
1. What is \((fh)(2)\) if \(f(x) = x^2 + 8x - 1\) and \(h(x) = 7 - 3x\)?
2. How would you find \(h(f(1))\)?
3. What are the intercepts of the function \(g(x) = -4x + 3\)?
4. How do you determine the composition \((gf)(x)\)?
5. What is the value of \((fg)(3)\)?

### Tip
Always work step-by-step, starting with inner functions in compositions to avoid errors.

If f(x)=x^2 + 8x − 1, g(x)=−4x + 3, and h(x)=7 − 3x, find (hg)(2).

Learn how to find the composition of two functions, g(x) = -4x + 3 and h(x) = 7 - 3x, by calculating (hg)(2). This detailed step-by-step solution covers important concepts such as function composition and linear functions, making it suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation