Jika f(x) = √(x²+1) dan (f o g) (x) = 1/(x-2) √(x²-4x+5) , maka g(x-3)=……

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a. 1/(x-5) b.1/(x+1) c.1/(x-1) d.1/(x-3) e.1/(x+3)

Jika f(x) = √(x²+1) dan (f o g) (x) = 1/(x-2) √(x²-4x+5) , maka g(x-3)=……

Jawaban Terkonfirmasi

Tentukan fungsi g(x) dengan:

$begin{align}(fcirc g)(x)&=frac1{x-2}sqrt{x^2-4x+5} \ f(g(x))&=sqrt{frac{x^2-4x+5}{(x-1)^2}} \ sqrt{[g(x)]^2+1}&=sqrt{frac{x^2-4x+5}{x^2-4x+4}} \ [g(x)]^2+1&=frac{x^2-4x+5}{x^2-4x+4} \ [g(x)]^2+1&=frac{x^2-4x+4}{x^2-4x+4}+frac{1}{x^2-4x+4} \ [g(x)]^2+1&=1+frac{1}{x^2-4x+4} \ [g(x)]^2&=frac{1}{(x-2)^2}~~to~~g(x)=frac1{x-2} \ g(x-3)&=frac{1}{(x-3)-2} \ g(x-3)&=frac1{x-5}end{align}