Composition of Functions

Addition

100

What does (f+g) (3) mean?

(OPORD)

You replace the x with a 3, solve, and then add them.

200

f(x) = 3x²+4 g(x) = x+3

Find (f+g)(x)

(f+g)(x) = 3x²+x+7

300

f(x) = 3x²-4 g(x) = x²+7x

Find (f+g)(x)

(f+g)(x) = 4x²+7x-4

400

f(x) = -2x²-7x+5 g(x) = 3x²+7x+3

Find (f+g)(3)

(f+g)(x) = 1x²+8

500

f(x) = -2x²-3x+4 g(x) = 2x²+3x-3

(f+g)(x) = 1

Subtraction

100

f(x) = 3x+3 g(x) = 2x+2

Find (f-g)(x)

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

200

f(x) = 7x²+6x+5 g(x) = 5x²+4x+3

Find (f-g)(x)

(f-g)(x) = 2x²+2x+2

300

f(x) = 4x²-3x g(x) = 5x²+3x

Find (f-g)(x)

(f-g)(x) = -1x²-6x

400

f(x) = -3x²-4x+5 g(x) = -3x²+1x-2

Find (f-g)(2)

(f-g)(x) = -5x+7

(f-g)(2) = -3

500

f(x) = -2x²-4x-5 g(x) = -4x²-4x+4

(f-g)(x) = 2x^2 -9

Multiplication

100

f(x) = 4x + 2 g(x) = 2x + 1

Find (f x g)(x)

(f x g)(x) = 8x² +8x+2

200

f(x) = 3x g(x) = -4x

Find (f x g)(x)

(f x g)(x) = -12x²

300

f(x) = 3x+4 g(x) = 2x+3

Find (f x g)(x)

(f x g)(x) = 6x²+17x+12

400

f(x) = 4x-3 g(x) = -3x+2

(f x g)(5) =

(f x g)(x) = -12x²+-1x-6

(f x g)(5) = -311

500

²(x) = -2x+4 g(x) = -3x-4

Find (f x g)(x)

(f x g)(x) = 6x²-4x-16

Composition

100

f(x) = 3x g(x) = -4

Find f(g(x))

f(g(x)) = -12

200

f(x) = 4x-5 g(x) = x-3

Find f(g(x))

f(g(x)) = 4x-17

300

f(x) = 6x-4 g(x) = 2x

Find g(f(x))

g(f(x)) = 12x-8

400

f(x) = 3x²-4 g(x) = 3x

Find f(g(3))

f(g(x)) = 3(3x)²-4

f(g(3)) = 239

500

f(x) = -3x²+5 g(x) = -2x+3

Find f(g(x))

(f(g(x)) = -3(-2x+3)²+5