Whats your function?

(f + g)(x) – add equations

(f – g)(x) – subtract equations

(f ●g)(x) – multiply

(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)

Your answer should be in factored form if possible

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

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

a. (x + 1) + (x^2 – 1)

x^2 + x

x (x + 1)

b. x + 1/x^2 – 1

x + 1/(x + 1) (x – 1)

1/(x – 1)

c. (x+1) (x^2 – 1)

(x+1)^2 (x – 1)

Ex 2: f(x) = x^4 – 3x^3 and g(x) = x – 2 Find (f ᵒ g) (x)

f (g(x)) = (x – 2)^4 – 3(x– 2)^3

(x –2)^3((x –2) – 3)

(x – 2)^3 (x – 5)

Ex 3: f(x) = 1/x and g(x) = x + 2 Find (f ᵒ g) (x) and (g ᵒ f) (x)

f(g(x)) = 1/(x + 2)

g(f(x)) = (1/x) + 2