Composition of Functions

Addition and Subtraction

100

Given f(x) = 2x²+4 g(x) = x+3, what is (f+g)(x)

2x²+x+7

200

Given f(x) = 3x²-4 g(x) = x²+7x+5, what is (f+g)(x)

4x²+7x + 1

300

Given f(x) = 3x²-5x+7 g(x) = -2x²+7x-3, 

what is (f-g)(x)

5x^{2 -} 12x + 10

400

f(x) = 2x² + 7x + 5 g(x) = 3x² + 7x + 3, 

what is (f-g)(x)

-x² + 2 

500

f(x) = 2x²-3x+4, g(x) = 2x²+3x-3, h(x) = 3x²-5x+1

What is (f+g-h)(x)

x² + 5x

Multiplication

100

f(x) = 3x+3,  g(x) = 2x+2 what is (fg)(x)

6x² +12x + 6

200

f(x) = 7x²+5 g(x) = 5x²+3

35x⁴ + 46x² + 15

300

f(x) = 4x²-3x+2 g(x) = 3x

12x³ -9x²+ 6x

400

f(x) = (x-2)²  g(x) = x²

x⁴ - 4x³ + 4x²

500

f(x) = 2x² + 3x -1 g(x) = x - 2

2x³ - x² - 7x + 2

Division

100

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

2/x

200

f(x) = 3x + 6 g(x) = 3

x + 2

300

f(x) = x² - 16 g(x) = x + 4

x - 4

400

f(x) = 6x² - x - 2 g(x) = 2x + 1

3x - 2

500

f(x) = x² - 3x - 4 g(x) = x² - x - 12

(x+1)/(x+3)

Composition

100

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

-12

200

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

4x-17

300

f(x) = x²-4 g(x) = x-3

x²- 6x + 5

400

f(x) = 3x²-4 g(x) = x + 1

3x² + 6x - 1

500

f(x) = 3x² + 5 g(x) = 2x - 1

12x² - 12x + 8

Challenge

100

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

what is (f+g+h)(x)

2x - 5

200

f(x) = x - 2 g(x) = 3x²  h(x) = -2x

what is (f*g + h)(x)

3x² - 6x - 2x

300

f(x) = x + 4 g(x) = 2x² - 7  h(x) = 2x + 5

what is (f-g-h)(x)

-x² - 2x + 6

400

f(x) = 2x² - 4   g(x) = x+1   h(x) = 5x

what is f(g(x)) + h(x)

2x² + 9x - 2

500

f(x) = x² + 4x + 4 g(x) = 2x - 4   h(x) = 3x

what is f(g(h(x))) 

36x² - 24x + 4