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Answer:
(f◦g)(x) = x
Step-by-step explanation:
The composition (f◦g)(x) means f(g(x)). As with any function evaluation, put the argument where the variable is, and simplify.
[tex](f\circ g)(x)=f(g(x))=f\left(\dfrac{3x}{x-1}\right)=\dfrac{\left(\dfrac{3x}{x-1}\right)}{\left(\dfrac{3x}{x-1}\right)-3}\\\\=\dfrac{\left(\dfrac{3x}{x-1}\right)}{\left(\dfrac{3x-3(x-1)}{x-1}\right)}=\dfrac{3x}{3x-3x+3}=\dfrac{3x}{3}\\\\\boxed{(f\circ g)(x)=x}[/tex]
