Operation and Composition of Functions

(f+g)(x)

100

f(x) = 3x²+4 g(x) = x+3

3x²+x+7

200

f(x) = 3x²-4 g(x) = x²+7x+5

4x² +7x+1

300

f(x) = 3x²-5x+7 g(x) = -2x²+7x-3

x²+2x+4

400

f(x) = -2x²-7x+5 g(x) = 3x²+7x+3

x²+8

500

f(x) = -2x²-3x+4 g(x) = 2x²+3x-3

1

(f-g)(x)

100

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

x+1

200

f(x) = 7x²+6x+5 g(x) = 5x²+4x+3

2x²+2x+2

300

f(x) = 4x²-3x+2 g(x) = 5x²+3x-2

-x²-6x+4

400

f(x) = -3x²-4x+5 g(x) = -3x²+5x-2

-9x+7

500

g(x) = -4x²-4x+4   f(x) = -2x²-4x-5 

2x²-9

(f*g)(x)

100

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

8x

200

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

-12x²

300

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

6x²+9x+8x+12 = 6x²+17x+12

400

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

-12x²+8x+9x-6=-12x²+17x-6

500

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

6x²+8x-12x-16 = 6x²-4x-16

f(g(x))

100

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

f(-4)=3(-4)=-12

200

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

f(x-3)=4(x-3)-5 = 4x-12-5

=4x-17

300

f(x) = 2x²-4 g(x) = x-3

f(x-3)=2(x-3)²-4

=2(x-3)(x-3)-4

=2(x²-6x+9)-4

=2x²-12x+14

400

f(x) = 3x²-4 g(x) = x-3

3(x-3)²-4

3(x-3)(x-3)-4

3(x²-6x+9)-4

3x²-18x+27-4

3x²-18x+23

500

f(x) = -3x²+5 g(x) = -2x+3

-3(-2x+3)(-2x+3)+5

-3(4x²-12x+9)+5

-12x²+36x-27+5

-12x²+36x-22

g(f(x))

100

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

g(4)=-4(4)=-16

200

f(x) = 2x g(x) = -3x²

g(2x)=-3(2x)²

=-3(2x)(2x)=-3(4x²)=-12x²

300

f(x) = x+4 g(x) = 2x²-7

2(x+4)²-7

2(x+4)(x+4)-7

2(x²+8x+16)-7

2x²+16x+32-7 = 2x²+16x+25

400

f(x) = 2x-4 g(x) = -3x²+1

-3(2x-4)(2x-4)+1

-3(4x²-16x+16)+1

-12x²+48x-47

500

f(x) = -3x+4 g(x) = x²-12

(-3x+4)(-3x+4)-12

9x²-24x+16-12

9x²-24x+4