Math Problem Statement

Given f(x) = 9x - 8 and g(x) = 5x - 3, find f(x) - g(x).

Solution

Let’s solve the problem from the image.

We are tasked with finding f(x)g(x)f(x) - g(x), given:

  • f(x)=9x8f(x) = 9x - 8
  • g(x)=5x3g(x) = 5x - 3

Step 1: Subtract g(x)g(x) from f(x)f(x)

f(x)g(x)=(9x8)(5x3)f(x) - g(x) = (9x - 8) - (5x - 3)

Step 2: Simplify the expression

Expand and combine like terms: f(x)g(x)=9x85x+3f(x) - g(x) = 9x - 8 - 5x + 3 f(x)g(x)=(9x5x)+(8+3)f(x) - g(x) = (9x - 5x) + (-8 + 3) f(x)g(x)=4x5f(x) - g(x) = 4x - 5

Final Answer:

4x5\boxed{4x - 5}

Would you like further details or explanations?


Here are five related questions you might find useful:

  1. What would f(x)+g(x)f(x) + g(x) be for the same functions?
  2. How do you find f(g(x))f(g(x)), the composition of ff and gg?
  3. What is the derivative of f(x)g(x)f(x) - g(x)?
  4. What happens if f(x)=g(x)f(x) = g(x)?
  5. Can you graph f(x)g(x)=4x5f(x) - g(x) = 4x - 5 and interpret its slope and y-intercept?

Tip: Always combine like terms carefully to avoid mistakes in sign or simplification!

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Simplification

Formulas

f(x) - g(x) = (9x - 8) - (5x - 3)

Theorems

Basic algebraic simplification

Suitable Grade Level

Grades 7-9