1.Diketahui g(x)=x²-3x dan gof(x)=x²+x-2 . Tentukan f(x) 2.Diketahui f(x)=x²+5x-3 dan gof(x)=2x²+10x-3 .Tentukan g(x)

jawab

1)
g(x)= x² - 3x
x² - 3x = y
(x  - 3/2)² = y  + 9/4
x - 3/2= √{1/4 (4y + 9)}
x = 3/2 + 1/2 √(4y + 9)
g⁻¹(x) =  1/2[3 +√(4x + 9)]

f(x)= g⁻¹ o (gof)(x)
f(x)=  g⁻¹{ gof(x)}
f(x)= 1/2 [ 3 + √{4(x²+x-2)+ 9}
f(x) = 1/2 [ 3 + √(4x² + 4x +1)
f(x)= 1/2[ 3 + √(2x+1)²]
f(x)= 1/2 [ 3 + 2x + 1]
f(x)= 1/2[ 4 + 2x]
f(x)= x + 2

2)
g{f(x)} = 2x² + 10 x - 3
g(x² + 5x - 3) = 2x² + 10 x - 3
g(x² + 5x - 3) = 2(x²+5x -3) +3
g(x)= 2x +3

Materi : Fungsi Komposisi




g(x) = x² - 3x
gof(x) = x² + x - 2
mka
gof(x) = x² + x - 2
          = = x² + 4x + 4 - 3x - 6
          = (x + 2)² - 3(x + 2)
hjadi f(x) = x + 2
          


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 f(x)=x² + 5x - 3 dan gof(x) = 2x² + 10x - 3

gof(x) = 2x² + 10x - 3
          = 2(x² + 5x - 3) - 3 + 6
          = 2(x² + 5x - 3) + 3

jadi g(x) = 2x + 3