Diketahui g(x) =x-1 dan (fog)(x)=2x²-7x+10, maka fungsi f(x) adalah? ​

Jawab:

fungsi komposisi
fog(x) =  f{ g(x)}

jika  g(x) =   x –  1 , dan  (fog)(x) = 2x² – 7x + 10

fog(x) = 2x² – 7x + 10
f{ g(x)} = 2x² – 7x + 10
f(x – 1) =  2x² – 7x + 10
f(x – 1) =  2(x – 1)² – 3(x – 1) +  5
f(x) =  2x² – 3x + 5

cara lain dengan  invers
fog(x) = 2x² – 7x + 10
f{ g(x)} = 2x² – 7x + 10
f(x – 1) =  2x² – 7x + 10  –> invers (x – 1) = ( x+ 1)
f(x) =  2 (x + 1)² – 7(x + 1) +10
f(x) = 2(x² +2x + 1) – 7x – 7 + 10
f(x) =  2x² + 4x  + 2 –  7x + 3
f(x) = 2x² –  3x + 5