diketahui fungsi f :r=r dan fungsi g :r=r ditentukan oleh rumus f (x) = 2x-3 dan g (x) =x kuadrat -x-2 tentukan: a.rumus fungsi (gof) x (x) dan (fog) (x) b. nil

f(x) = 2x - 3
g(x) = x² - x - 2

a) (fog) (x) dan (gof) (x)
(fog) (x) = f(x² - x - 2)
(fog) (x) = 2(x² - x - 2) - 3
(fog) (x) = 2x² - 2x - 4 - 3
(fog) (x) = 2x² - 2x - 7

(gof) (x) = (2x - 3)² - (2x - 3) - 2
(gof) (x) = 4x² - 12x + 9 - 2x + 3 - 2
(gof) (x) = 4x² - 14x + 10

B) (gof) (-4) = 4(-4)² - 14(-4) + 10
(gof) (-4) = 64 + 56 + 10
(gof) (-4) = 130

C) (fog) (4) = 2(4)² - 2(4) - 7
(fog) (4) = 32 - 8 - 7
(fog) (4) = 17

Diket :
f(x)= 2x-3
g(x)= x²-x-2
ditanya :
a.) rumus (gof) (x) Dan (fog) (x)...?
b.) (gof) (-4)...?
c.) (fog) (4)...?
jawab :
a.) (gof) (x)
= g(fx)
= g(2x-3)
= (2x-3)²-(2x-3)-2
= (2x-3)(2x-3)-2x+3-2
= 4x²-6x-6x+9-2x+1
= 4x²-14x+10
(fog) (x)
= f(gx)
= f(x²-x-2)
= 2(x²-x-2)-3
= 2x²-2x-4-3
= 2x²-2x-7
b.) (gof) (-4)
= g(f-4)
= g(2.-4 - 3)
= g(-8-3)
= g(-11)
= (-11)²-(11)-2
= 121-11-2
= 108
c.) (fog) (4)
= f(g4)
= f(4²-4-2)
= f(16-4-2)
= f(10)
= 2(10)-3
= 20-3
= 17

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