Math Problem Statement

What is the value of (f - g)(5)?

Solution

The problem asks for the value of (fg)(5)(f - g)(5), where f(x)f(x) and g(x)g(x) are given in two tables.

Let's break it down:

We know that: (fg)(x)=f(x)g(x)(f - g)(x) = f(x) - g(x)

To find (fg)(5)(f - g)(5), we need to subtract the value of g(5)g(5) from f(5)f(5).

From the tables:

  • f(5)=29f(5) = 29
  • g(5)=13g(5) = 13

Thus, (fg)(5)=f(5)g(5)=2913=16(f - g)(5) = f(5) - g(5) = 29 - 13 = 16

So, the value of (fg)(5)(f - g)(5) is 16.

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:

  1. What is the value of (f+g)(1)(f + g)(1)?
  2. How do you find (fg)(5)(f \cdot g)(-5)?
  3. What is (f/g)(2)(f/g)(-2) if g(2)0g(-2) \neq 0?
  4. How would you find the derivative of f(x)g(x)f(x) - g(x) if you had the functions f(x)f(x) and g(x)g(x)?
  5. Can you determine a zero for f(x)g(x)f(x) - g(x)?

Tip: When solving for the difference of functions, make sure to use the values from the same xx-coordinate for both functions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Operations

Formulas

(f - g)(x) = f(x) - g(x)

Theorems

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Suitable Grade Level

Grades 7-9