Matematika

Pertanyaan

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1 Jawaban

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    [tex]\displaystyle (g\circ f)(x)=\frac{x-6}{x+4},f(x)=x+2 \\ g(f(x))=\frac{x-6}{x+4} \\ g(x+2)=\frac{x-6}{x+4} \\ g(x)=\frac{(x-2)-6}{(x-2)+4}=\frac{x-8}{x+2} \\ g(4)=\frac{4-8}{4+2}=\frac{-4}{6}=-0.666...[/tex]

    [tex]\displaystyle f(x)=\frac{2x+1}{x}, (f\circ g)(x)=x-2 \\ f(g(x))=x-2 \\ \frac{2.g(x)+1}{g(x)}=x-2 \\ 2.g(x)+1=x.g(x)-2.g(x) \\ 4.g(x)-x.g(x)=-1 \\ g(x) (4-x)=-1 \\ g(x)=\frac{-1}{4-x}=\frac{1}{x-4} \\ g(3)=\frac{1}{3-4}=\frac{1}{-1}=-1[/tex]