Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 62

$(f\circ f) (x)=x$

We have $f(x)=\dfrac{x}{x-1}$ We simplify the composite function as: $(f\circ f) (x) =f[f(x)] \\ =f [\dfrac{x}{x-1}] \\ =\dfrac{\frac{x}{x-1}}{\dfrac{x}{x-1}-1}\\=\dfrac{x}{x -(x-1)} \times \dfrac{x-1}{x-1} \\ =\dfrac{x}{x-x+1}\\=\dfrac{x}{1}\\ =x$ Therefore, $(f\circ f) (x)=x$