Diketahui f(x)=2 x+3, g(x)=3 x-1 , dan (h o g o

Nilai $h(0)$ adalah $rac{7}{24}$.

Pembahasan

Diketahui:
$f(x) = 2x + 3$
$g(x) = 3x - 1$
$(h 	ext{ o } g 	ext{ o } f)(x) = rac{x^2 - 1}{x + 4}$

Kita perlu mencari nilai $h(0)$.

Langkah 1: Cari $(g 	ext{ o } f)(x)$.
$(g 	ext{ o } f)(x) = g(f(x)) = g(2x + 3)$
$(g 	ext{ o } f)(x) = 3(2x + 3) - 1$
$(g 	ext{ o } f)(x) = 6x + 9 - 1$
$(g 	ext{ o } f)(x) = 6x + 8$

Langkah 2: Cari $(h 	ext{ o } g 	ext{ o } f)(x)$.
$(h 	ext{ o } g 	ext{ o } f)(x) = h((g 	ext{ o } f)(x)) = h(6x + 8)$
Kita tahu bahwa $(h 	ext{ o } g 	ext{ o } f)(x) = rac{x^2 - 1}{x + 4}$.
Jadi, $h(6x + 8) = rac{x^2 - 1}{x + 4}$.

Langkah 3: Tentukan nilai $x$ agar $6x + 8 = 0$ untuk mencari $h(0)$.
$6x + 8 = 0$
$6x = -8$
$x = -rac{8}{6} = -rac{4}{3}$

Langkah 4: Substitusikan nilai $x = -rac{4}{3}$ ke dalam persamaan $h(6x + 8) = rac{x^2 - 1}{x + 4}$.
$h(6(-rac{4}{3}) + 8) = rac{(-rac{4}{3})^2 - 1}{(-rac{4}{3}) + 4}$
$h(-8 + 8) = rac{rac{16}{9} - 1}{-rac{4}{3} + rac{12}{3}}$
$h(0) = rac{rac{16}{9} - rac{9}{9}}{rac{8}{3}}$
$h(0) = rac{rac{7}{9}}{rac{8}{3}}$
$h(0) = rac{7}{9} 	imes rac{3}{8}$
$h(0) = rac{21}{72}$
$h(0) = rac{7}{24}$

Jadi, nilai $h(0)$ adalah $rac{7}{24}$.