Operations on Functions

Introduction

• Topic: Operations on Functions (General Mathematics - Grade 11)
• Covered Operations: Sum, Difference, Product, Quotient

Key Concepts

Sum of Functions

• Notation: f + g of x
• Formula: f(x) + g(x)

Difference of Functions

• Notation: f - g of x
• Formula: f(x) - g(x)

Product of Functions

• Notation: f * g of x
• Formula: f(x) * g(x)

Quotient of Functions

• Notation: f / g of x
• Formula: f(x) / g(x)
• Condition: g(x) should not be zero to avoid undefined results

Example: Given Functions

• f(x) = x^2 - 1
• g(x) = x^2 - x

Sum of Functions

• f + g of x = (x^2 - 1) + (x^2 - x)
• Steps:
  • Add similar terms (x^2 with x^2, constants with constants)
  • Result: 2x^2 - x - 1

Difference of Functions

• f - g of x = (x^2 - 1) - (x^2 - x)
• Steps:
  • Change operation from subtraction to addition
  • Change signs of g(x) terms
  • Combine similar terms
  • Result: x - 1

Product of Functions

• f * g of x = (x^2 - 1) * (x^2 - x)
• Steps:
  • Use FOIL Method (First, Outer, Inner, Last)
  • Result: x^4 - x^3 - x^2 + x

Quotient of Functions

• f / g of x = (x^2 - 1) / (x^2 - x)
• Steps:
  • Factor the numerator and denominator
  • Simplify common factors
  • Result: (x + 1) / x

Conclusion

• Review of operations on functions
• Encourage questions in comments
• Sign off by Prof. D