Function Notation

Function Notations (as the title suggests):

(f + g)(x) - add equations

(f – g)(x) - subtract equations

(f ●g)(x) - multiply equations

(f/g)(x) - divide equations

(f ᵒ g)(x) or f(g(x)) – replace all x’s in the f(x) equation with the equation g(x)
I think of the little open circle thing as an o, standing for the word "of". f of g of x, or f(g(x)), with every set of parentheses meaning "of".

You should factor your final answer. Or the goblins might get you.

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

Ex. 1
f(x) = 2x+3 g(x) = 4x²-9

Find:
a. (f+g)(x)
2x+3 + 4x²-9
4x²+2x-6
4x²-4x+6x-6
4x(x-1)+6(x-1)

(4x+6)(x-1)

b. (f-g)(x)
2x+3 - ( 4x²-9)
-4x²+2x+12
4x²-2x-12
4x²-8x+6x-12
4x(x-2)+6(x-2)

(4x+6)(x-2)

c. (f ●g)(x)
(2x+3)(4x²-9)
Instead of FOILing it out, I'm going to factor it.
(2x+3)(2x+3)(2x-3)

(2x+3)² (2x-3)

d. (f/g)(x)
2x+3/4x²-9
You can factor the denominator:
2x+3/(2x-3)(2x+3) and cancel:

1/2x-3

e. (f ᵒ g)(x)
2(4x²-9)+3
8x²-18+3

8x²-15