Diketahui f(x) = 2x-3/x+4, (gof)(x)= x²- 7 +8. Carilah g(3).

Jawab:

1.)F(x) = x² + 2x + 3

g(x) = 2x – 3

(gof)(x) = g(f(x))

= 2(x² + 2x + 3) – 3

= 2x² + 4x + 6 – 3

(gof)(x) = 2x² + 4x +3

(gof)(a) = 19

(gof)(a) = 2a² + 4a + 3

19 = 2a² + 4a + 3

2a² + 4a – 16 = 0

a² + 2a – 8 = 0

(a – 2)(a + 4) = 0

a – 2 = 0 atau a + 4 = 0

a=2

a=-4

2.)Fog(x)=x²+3x +1

F(g(x)=x² +3x +1

F(x+1)=x² +3x +1

Misal x + 1=a,sehingga x=a – 1

F(a)=(a-1)²+3(a-1)+1

F(x)=(x-1)²+3(x-1)+1

F(x)=x²-2x + 1+ 3x – 3 + 1

F(x)=x² + x + 1

4.)Gof(x)= g(f(x))  

= g(2-x)

= (2-x)^2+1

gof(x) =x^2-4x+5

hogof(x)=h(g(f(x))

6 = h(x^2-4x+5)

3(x^2-4x+5) = 6

x^2-4x+5 = 2

x^2-4x+3 =0

(x-1) (x-3) =0

x1=1 x20

6.)f(x) = (4x – 2)/(x + 1)

f(2) = (4 . 2 – 2)/(2 + 1)

f(2) = 6/3

f(2) = 2

g(x) = x³ + x² – 7x + 5

g(2) = 2³ + 2² – 7. 2 + 5

g(2) = 8 + 4 – 14 + 5

g(2) = 3

(gof) (2) = 3

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