Math Problem Statement

Find (f - g)(x) where f(x) = 3x + 3 and g(x) = -4x + 1

Solution

From the image, you have the functions:

f(x)=3x+3f(x) = 3x + 3 g(x)=4x+1g(x) = -4x + 1

You are asked to find (fg)(x)(f - g)(x), which means the difference between the two functions, i.e.,

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

Let's compute it:

(fg)(x)=(3x+3)(4x+1)(f - g)(x) = (3x + 3) - (-4x + 1)

Simplifying:

(fg)(x)=3x+3+4x1(f - g)(x) = 3x + 3 + 4x - 1 (fg)(x)=(3x+4x)+(31)(f - g)(x) = (3x + 4x) + (3 - 1) (fg)(x)=7x+2(f - g)(x) = 7x + 2

Thus, the result is:

(fg)(x)=7x+2(f - g)(x) = 7x + 2

Would you like more details or further explanation?

Here are five related questions to expand your understanding:

  1. What is (f+g)(x)(f + g)(x) based on the given functions?
  2. How would you find (fg)(x)(f \cdot g)(x), the product of f(x)f(x) and g(x)g(x)?
  3. How can you compute the composite function f(g(x))f(g(x))?
  4. What is the inverse of f(x)=3x+3f(x) = 3x + 3?
  5. How do you find the x-intercept of (fg)(x)(f - g)(x)?

Tip: When subtracting two functions, be sure to distribute the negative sign to all terms in the second function before simplifying.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Subtraction of Functions

Formulas

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

Theorems

None needed, basic algebra

Suitable Grade Level

Grades 9-10