1) suatu fungsi ax + b , dengan f(1) = 5 , f(2) = 1 , tentukan : a. nilai a dan b 2) suatu fungsi f(x) = 3x - 6 , tentukan rumus fungsi yang paling sederhana da

Jawab :

1) f(x) = ax + b
f(1) = a(1) + b
      = 1a + b = 5

f(x) = ax + b
f(2) = a(2) + b 
      = 2a + b = 1

1a + b = 5
2a + b = 1
_________ - 
-1a     = 4
a        = 4/-1
a        = -4

2a + b = 1
2(1) + b = 1
2 + b = 1
b       = 1 - 2
b       = -1

2) a. f(x) = 3x - 6
f(x - 1) = 3(x - 1) - 6
           = 3x - 3 - 6
f(x - 1) = 3x - 9

b. f(x) = 3x - 6
f(-x + 3) = 3(-x + 3) - 6
              = 3x - 9 - 6
f(-x + 3) = 3x - 15

3) (3x - 4) - (2x - 10)
= 3x - 4 - 2x + 10
= x + 6

4) 2(x² + 8x)
= 2x² + 16x

5) (x + 4) (x + 3)
= x² + 3x + 4x + 12
= x² + 7x + 12

6) m = 4 , melalui titik (2,3)

y - y1 = m(x - x1)
y - 3 = 4(x - 2)
y - 3 = 4x - 8
y = 4x - 8 + 3
y = 4x + 5

7) m = 2 , melalui titik (5,2)

y - y1 = m(x - x1)
y - 2 = 2(x - 5)
y - 2 = 2x - 10
y = 2x - 10 + 2
y = 2x - 8

1)f(1)= 1a+b=5
f(2)=2a+b=1
_________ -
-a = -2
a = 2
4+b=5
b=5-4 jadi a=2
=1. b=1

2). a.)f(x-1)=3(x-1)-6
=3x-3-6
=3x-9

b.)f(-x+3)=3(-x+3)-6
=-3x+9-6
= -3x+3

3.) (3x-4) - (2x-10)
=-6x-30x+8x+40
= -16x+40

4) 2(x²+8x)
= 2x²+16x

5)(x+4)(x+3)
=x²+3x+4x+12
=x²+7x+12

6)y-y1=m(x-x1)
y-3=4(x-2)
y-3=4x-8
y-4x-3+8=0

7)y-y1=m(x-x1)
y-2=2(x-5)
y-2=2x-10
y-2x-2+10=0