Matematika

Pertanyaan

Kak adek ada tugas tentang fungsi komposisi pertanyaan dari soal berikut tentukan:
f(x)=x²+2
g(x)=x²+1
h(x)=x+1
1.(h°g°f) (x)=
2. (h°g°f) (-1)=
3. (f°g°h) (x)=
4(f°g°h) (-2)=

1 Jawaban

  • (hogof)(x)
    = h(gof)
    = (gof)+1
    = ((x²+2)²+1)+1
    = (x⁴+4x²+4+1)+1
    = x⁴+4x²+6

    (hogof)(-1)
    = x⁴+4x²+6
    = (-1)⁴+4(-1)²+6
    = 11

    (fogoh)(x)
    = f(goh)
    = (goh)²+2
    = ((x+1)²+1)+2
    = (x²+2x+1+1)+2
    = x²+2x+4

    (fogoh)(-2)
    = x²+2x+4
    = (-2)²+2(-2)+4
    = 4-4+4
    = 4

Pertanyaan Lainnya