Function Notation

f(x) = x^2 + 5x - 2 is an example of a function. If it says "Evaluate f(2)", you can assume x = 2 and plug in 2 for all x's in the function and simplify. Here are some other things you can do with functions:

(f+g)(x) = f(x) + g(x)
(f-g)(x) = f(x) - g(x)
(f*g)(x) = f(x) * g(x)
(f/g)(x) = f(x) / g(x)
(f○g)(x) = f(g(x)) or plug in the equation g(x) into all x's in f(x)
(g○f)(x) = g(f(x)) or plug in the equation f(x) into all x's in g(x)


Ex. 1

f(x) = 3x+3
g(x) = x-8

Evaluate f(2)
f(2) = 3(2)+3
= 6+3
= 9

Evaluate g(3)
g(3) = (3)-8
= -5


Ex. 2
f(x) = 2x-8
g(x) = x^2 +4

Find (f+g)(x)
2x-8 + (x^2 + 4)
x^2 + 2x -4

Find (f-g)(x)
2x-8 - (x^2 + 4)
2x - 8 - x^2 - 4
-x^2 + 2x - 12

Find (f*g)(x)
(2x-8)(x^2+4)
2x^3+8x-8x^2-32
2x^3-8x^2+8x-32

Find (f/g)(x)
(2x-8)/(x^2+4)

Find (f○g)(x)
2(x^2+4) - 8
2x^2+8-8
2x^2

Find (g○f)(x)
(2x-8)^2 +4
4x^2-32x+64+4
4x^2-32x+68


Ex. 3
f(x) = 2x^2 -1
g(x) = x+1

Find (f○g)(2)
2(2+1)^2 -1
2(3)^2 - 1
2(9) - 1
18 - 1
17

Find (g○f)(2)
(2(2)^2 -1) +1
2(4) -1 +1
8 -1 +1
8

Find (g*f)(1)
(1+1)(2(1)^2-1)
(2)(2-1)
(2)(1)
2

Find (f+g)(8)
2(8)^2 - 1 + 8 + 1
2(64)-1+8+1
128+8
136

Find (f-g)(6)
2(6)^2 -1 -(6+1)
2(36) - 1 - 7
72 -8
64