Page 95 - Matematika kelas 10

(g(fh)(x)) = (gk)(x)

= g(k(x))
= 4(k(x)) + 5

= 4(4x – 7) + 5

= 16x – 28 +5

= 16x – 23

Jadi, fungsi komposisi (g(fh)(x)) = 16x – 23
ii) Misalkan l(x) = (gf)(x)

l(x) = g(f(x)) = 4(f(x)) + 5

= 4(2x – 1) + 5

= 8x – 4 + 5

= 8x + 1

((gf)h)(x) = (lh)(x)

= l(h(x))
= 8(h(x)) + 1

= 8(2x – 3) + 1

= 16x – 24 + 1

= 16x – 23

Jadi, rumus fungsi komposisi ((gf)h)(x) = 16x – 23.
b) Rumus fungsi komposisi (f(gh))(x) dan ((fg)h)(x)

i) Misalkan m(x) = (gh)(x)

m(x) = g(h(x)) = 4(h(x)) + 5

= 4(2x – 3) + 5
= 8x – 12 + 5

= 8x – 7

Matematika 93