Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 42

See below.

Given $f(x)=\frac{x-5}{2x+3}$ and $g(x)=\frac{3x+5}{1-2x}$, we have: 1. $f(g(x))=\frac{(\frac{3x+5}{1-2x})-5}{2(\frac{3x+5}{1-2x})+3}=\frac{3x+5-5+10x}{6x+10+3-6x}=x$, with $x\ne\frac{1}{2}$ 2. $g(f(x))=\frac{3(\frac{x-5}{2x+3})+5}{1-2(\frac{x-5}{2x+3})}=\frac{3x-15+10x+15}{2x+3-2x+10}=x$, with $x\ne-\frac{3}{2}$