Chapter 5 - Trigonometric Functions - Section 5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions - 5.5 Assess Your Understanding - Page 442: 48

$(f\circ g)(x)=csc(x)$ and $(g\circ f)(x)=2csc(\frac{1}{2}x)$. See graph.

1. Given $f(x)=\frac{1}{2}x$ and $g(x)=2csc(x)$, we have $(f\circ g)(x)=\frac{1}{2}(2csc(x))=csc(x)$ and $(g\circ f)(x)=2csc(\frac{1}{2}x)$. 2. See graph for $(f\circ g)(x$ (red) and $(g\circ f)(x)$ (blue).