operations on functions

1
operations on functions

• sum (f g)(x)
• difference (f - g)(x)
• product (f g)(x)
• quotient (f / g)(x)

domain of functions

• Domain is formed by intersection of domains of f
  and g,
• Domain of f/g is same except all x such that g(x)
  0

2
Sum (f g)(x) f(x) g(x)

• f(x) x 2 - 25 g(x) x - 5
• (f g)(x) (x 2 - 25) (x - 5)
• x 2 x - 30
• Domain (-8,8)

3
difference (f - g)(x) f(x) - g(x)

• f(x) x 2 25 g(x) x - 5
• (f - g)(x) (x 2 - 25) - (x - 5)
• x 2 - 25 - x 5
• x 2 - x - 20
• Domain (-8,8)

4
Product(f g)(x) f(x) g(x)

• f(x) x 2 25 g(x) x - 5
• (f g)(x) (x 2 - 25) (x - 5)
• x 3 - 5x 2 - 25x 125
• Domain (-8,8)

5
Quotient(f / g)(x) f(x) g(x) g(x) ? 0

• f(x) x 2 25 g(x) x - 5
• (f / g)(x) (x 2 - 25) / (x - 5)
• x 5
• Domain xx ? 5