Let \(f(x)=log (x^2-2x)\) and \(g(x) = \frac{x}{x-1}\). Which expression represents \(f(g(x)\) ?
a) \(log (\frac{x^3 -2x^2}{x-1})\)
b) \(log(\frac{x^2-2x(x-1)}{(x-1)^2})\)
c) \(\frac{log(x^2-2x)}{log(x^2-2x)-1}\)
d) \(\frac{xlog(x^2-2x)}{x-1}\)
f(g (x) ) = log [ (x)^2 / ( x - 1)^2 - 2x / (x - 1) ] =
x^2 - 2x ( x - 1)
log ____________ = "b"
(x - 1)^2
Thank you so much!