Respuesta :

Leukonov

(f°g)(x)=f(g(x))

g(x)=x/(x-1)

so(f(g(x)) =f([x/(x-1)])

[tex] log( { (\frac{x}{x - 1}) }^{2} \: - \: 2 \frac{x}{x - 1} ) \\ = log( \frac{ {x}^{2} - 2x(x - 1) }{ {(x - 1)}^{2} } ) [/tex]

Hence; answer is option C.

The composition means

[tex](f\circ g)(x) = f(g(x))[/tex]

So, we have

[tex]g(x) = \dfrac{x}{x-1}[/tex]

If we have to compute f with this input, we have

[tex]f\left(\dfrac{x}{x-1}\right) = \log\left(\dfrac{x^2}{(x-1)^2}-\dfrac{2x}{x-1}\right)[/tex]

we can simplify this expression as follows

[tex]\log\left(\dfrac{x^2-2x(x-1)}{(x-1)^2}\right)[/tex]

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