Math Problem Statement

Evaluate the function (f - g)(x) for x = -5, given f(x) = -3x, g(x) = |x - 4|, and h(x) = 1/(x + 7).

Solution

Let's analyze the given functions and the problem.

Given Functions:

  1. f(x)=3xf(x) = -3x
  2. g(x)=x4g(x) = |x - 4|
  3. h(x)=1x+7h(x) = \frac{1}{x + 7}

Task:

Evaluate the function (fg)(x)(f - g)(x) for x=5x = -5.

Calculation:

  1. Find f(5)f(-5): f(5)=3(5)=15f(-5) = -3(-5) = 15

  2. Find g(5)g(-5): g(5)=54=9=9g(-5) = |-5 - 4| = |-9| = 9

  3. Find (fg)(5)(f - g)(-5): (fg)(5)=f(5)g(5)=159=6(f - g)(-5) = f(-5) - g(-5) = 15 - 9 = 6

Therefore, (fg)(5)=6(f - g)(-5) = 6.

The error in the given image is because the calculated value of (fg)(5)(f - g)(-5) is shown as 7-7, which is incorrect. The correct answer should be 6.

Would you like more details or have any questions?

Related Questions:

  1. What is the value of (fg)(x)(f \cdot g)(x) for x=5x = -5?
  2. How would you find (f+g)(x)(f + g)(x) for any xx?
  3. What is the domain of the function h(x)h(x)?
  4. How does the graph of g(x)=x4g(x) = |x - 4| look like?
  5. Can h(x)h(x) be evaluated for x=7x = -7?

Tip: Always double-check calculations and the interpretation of functions, especially when absolute values and subtractions are involved.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Functions
Linear Functions

Formulas

f(x) = -3x
g(x) = |x - 4|
(f - g)(x) = f(x) - g(x)

Theorems

Properties of Absolute Values
Operations with Functions

Suitable Grade Level

Grade 9-11