nomer 4 sama 5 (a dan b), belom dijelasin jd bingung bgt, sekalian caranya yahhh :3
yang bisa mintol bgt yaa^^ thankss <3
> MATERI: Fungsi Komposisi
Ingat kembali konsep dasar fungsi komposisi:
[tex]\boxed{\begin{minipage}{3 cm}$(f \circ g)(x) = f(g(x))\\(g \circ f)(x) = g(f(x))$\end{minipage}}[/tex]
> SOAL NO. 4:
Diketahui:
[tex]f(x)=2x^2+3x-5[/tex]
[tex]g(x)=3x-2[/tex]
[tex](g \circ f)(a) = -11[/tex]
Ditanya:
[tex]a = \; ? \; \; \textbf{\textit{(yang positif)}}[/tex]
Jawab:
[tex]\begin{array}{r c l}(g \circ f)(a) & = & -11\\\\g(f(a)) & = & -11\\\\g(2a^2+3a-5) & = & -11\\\\3(2a^2+3a-5)-2 & = & -11\\\\6a^2+9a-15-2 & = & -11\\\\6a^2+9a-17 & = & -11\\\\6a^2+9a-6 & = & 0\\\\2a^2+3a-2 & = & 0\\\\(2a - 1)(a + 2) & = & 0\\\end{align}[/tex]
[tex]\boxed{a = \frac{1}{2} \; \; \textbf{\textit{atau}} \; \; a = -2}[/tex]
Karena pada soal yang diminta adalah nilai yang positif, maka nilai a yang memenuhi adalah 1/2.
> SOAL NO. 5 (a):
Diketahui:
[tex]f(x)=x-5[/tex]
[tex]g(x)=x^2-1[/tex]
[tex](f \circ g)(x) = 3[/tex]
Ditanya:
[tex]x = \; ?[/tex]
Jawab:
[tex]\begin{array}{r c l}(f \circ g)(x) & = & 3\\\\f(g(x)) & = & 3\\\\f(x^2-1) & = & 3\\\\(x^2 - 1)-5 & = & 3\\\\x^2-6 & = & 3\\\\x^2-9 & = & 0\\\\(x+3)(x-3) & = & 0\\\end{align}[/tex]
[tex]\boxed{x = -3 \; \; \textbf{\textit{atau}} \; \; x = 3}[/tex]
Jadi, himpunan nilai x yang memenuhi adalah {-3, 3}.
> SOAL NO. 5 (b):
Diketahui:
[tex]f(x)=x-5[/tex]
[tex]g(x)=x^2-1[/tex]
[tex](g \circ f)(x) = 0[/tex]
Ditanya:
[tex]x = \; ?[/tex]
Jawab:
[tex]\begin{array}{r c l}(g \circ f)(x) & = & 0\\\\g(f(x)) & = & 0\\\\g(x-5) & = & 0\\\\(x-5)^2-1 & = & 0\\\\x^2 - 10x + 25 - 1 & = & 0\\\\x^2 - 10x + 24 & = & 0\\\\(x-4)(x-6) & = & 0\\\end{align}[/tex]
[tex]\boxed{x = 4 \; \; \textbf{\textit{atau}} \; \; x = 6}[/tex]
