Problem: let f(x)=log(x^2-2x) and g(x)=x/x-1. which expression represents (fog)(x)?
Solution:
notice that:
[tex](f\circ g)(x)\text{ = f(g(x))}[/tex]then, the composition would be:
[tex](f\circ g)(x)\text{ = f(g(x)) = log( (}\frac{x}{x-1})^2-2\text{(}\frac{x}{x-1})\text{ )}[/tex]this is equivalent to
[tex]=\text{ log( }\frac{x^2}{(x-1)^2}^{}-\frac{2x}{x-1}\text{)}[/tex]this is equivalent to (Making common factor):
[tex]=\text{ log( }\frac{x^2-2x(x-1)}{(x-1)^2})[/tex]then the correct answer would be:
[tex]=\text{ log( }\frac{x^2-2x(x-1)}{(x-1)^2})[/tex]