Question

Diketahui g(x)=2x+1,fog(x)=x²+x tentukan f(x)

Answer 1

Fog (x) = x2 + x
f (g (x))= x2 + x
f ( 2x + 1 ) = x2 + x
dimisalkan a = 2x + 1
maka x =( a-1) /2
dengan demikian
f (a) = ((a-1) / 2)^2 + (a-1) / 2
f (a) = (a2-2a+1)/4 + (a-1) / 2
f (a) = (a2-2a+1)/4 + 2(a-1) / 4
f (a) = (a2-2a+1+2a-2)/4
f (a) = (a2-1)/4
f (a) = 1/4 ( a2 -1 )
maka,
f (x) = 1/4 ( x2 -1 )

semoga membantu.