F(x-5) =3x^+2x, f(x)?.... Question from @fitrohainaf

October 2018 2 54 Report

F(x-5) =3x^+2x, f(x)?

ekamiaww F(x-5) = 3x² + 2x
misal: x - 5 = a
x = a + 5
f(a) = 3 (a + 5)² + 2 (a + 5)
f(a) = 3 (a² + 10a + 25) + 2a + 10
f(a) = 3a² + 30a + 75 + 2a + 10
f(a) = 3a² + 32a + 85
f(x) = 3x² + 32x + 85

semoga membantu ya :)

1 votes Thanks 1

fatihahalhusna good job, saya coba beri solusi yang lain, lihat di bawah ya

fatihahalhusna Misalkan:
$F(x)=ax^2+bx+c$
maka:
$F(x-5)=a(x-5)^2+b(x-5)+c$
$3x^2 + 2x= a(x^2-10x+25)+bx-5b+c$
$3x^2 + 2x= ax^2-10ax+25a+bx-5b+c$
$3x^2 + 2x= ax^2-(10a-b)x+25a--5b+c$
berdasarkan kesamaannya kita peroleh:
$a=3$
$-(10a-b)=2$ $~\rightarrow~-(10.3-b)=2~\righarrow~~b=32$
$25a-5b+c=0~\rightarrow~~25.3-5.32+c=0$
$75-160+c=0~\rightarrow~c=85$
Jadi: $\boxed{F(x)=3x^2+32x-85}$

1 votes Thanks 2

ekamiaww mantabb.. super.. :)

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