Fuction notation

(f + g)(x) – add equations

(f – g)(x) – subtract equations

(f • g)(x) – multiply(closed circle)

(f/g)(x) – divide

(f ᵒ g)(x) or f(g(x)) – replace all x’s in the f(x) equation with the equation g(x)

If x is replaced with a number, plug into the equation

Ex: f(2); (f + g)(2); etc.

Ex 1. f(x) = x + 1 g(x) = x^2 – 1 Find the rule for a. (f + g)(x) b. (f/g)(x)

a. (x + 1) + (x^2 – 1) b. x + 1/x^2 – 1 = x + 1/( x + 1)(x – 1)

x^2 + x = x(x + 1) = 1/x – 1

Ex 2. f(x) = x^4 – 3x^2 g(x) = sqrtx – 2 Find (f ᵒ g)(x)

f(g(x)) = (sqrtx – 2)^4 – 3(sqrtx – 2)^2

(x – 2)^2 – 3(x – 2) = (x – 2)((x – 2) – 3) = (x – 2)( x – 5)

Ex 3. f(x) = 1/x g(x) = x + 1 Find (f ᵒ g)(x) and ( g ᵒ f)(x)

f(g(x)) = 1/x + 1 g(f(x)) = 1/x + 1