Arithmetic of Functions

Add/Subtract Functions

100

ADD f(x)= 3x²+4 and    g(x) = x+3

3x²+x+7

200

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

x+1

300

ADD f(x) = 3x²-5x+7 and g(x) = -2x²+7x-3

x²+2x+4

400

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

1

500

SUB g(x) = -4x²-4x+4 and f(x) = -2x²-4x-5

-2x²+9

Multiply/Divide Functions

100

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

8x

200

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

2⁄x

300

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

6x²+17x+12

400

MULTIPLY f(x)=4x²-3 and g(x) =-3x+2

-12x³+8x²+9x-6

500

DIVIDE f(x) = x²−3x−40 and g(x) = x - 8

x+5

Compositions of Functions Level 2

100

g(f(0)) when f(x)=3x²+x-6 and g(x)=-4x-3

21

200

g(f(1)) when f(x)=2x²+4x+4 and g(x)=2x+7

27

300

f(g(0)) when f(x)=3x²+x-6 and g(x)=-4x-3

18

400

(g ∘ f)(2) when 

f(x)=-x+2 and g(x)=x²-x-5

-5

500

(f ∘ g)(2) when     

f(x)=-x+2and g(x)=x²-x-5

5

Compositions of Functions Level 3

100

f(g(x)) when f(x) = 4x and g(x) = -5x

-20x

200

g(f(x)) when f(x) = 2x and g(x) = -3x²

-12x²

300

(f ∘ g)(x) when f(x) = x+4 and g(x) = 2x²-7

2x²-3

400

(g ∘ f)(x) when f(x) = x+4 and g(x) = 2x²-7

2x²+16x+25

500

g(f(x)) when f(x) = x-1 and g(x)=3x²-4x-12

3x²-10x-5