83.

1. 

2. No

3. Domain: $[-2,\text{ 2}];$ Range: [0, 2]

85.

1. 

2. $f{}^{-1}(x)={\displaystyle \frac{x}{1-x}}$

3. Domain: $(-\infty ,-1)\cup (-1,\infty );$ range: $(-\infty ,1)\cup (1,\infty )$

f satisfies the horizontal-line test.

87.

1. 1. $f{}^{-1}(x)={\displaystyle \frac{1}{2}}x+{\displaystyle \frac{1}{2}}$

   2. $g^{-1}(x)={\displaystyle \frac{1}{3}}x-{\displaystyle \frac{4}{3}}$

   3. $(f\circ g)(x)=6x+7$

   4. $(g\circ f)(x)=6x+1$

   5. ${(f\circ g)}^{-1}(x)={\displaystyle \frac{1}{6}}x-{\displaystyle \frac{7}{6}}$

   6. ${(g\circ f)}^{-1}(x)={\displaystyle \frac{1}{6}}x-{\displaystyle \frac{1}{6}}$

   7. $(f^{-1}\circ g^{-1})(x)={\displaystyle \frac{1}{6}}x-{\displaystyle \frac{1}{6}}$

   8. $(g^{-1}\circ f^{-1})(x)={\displaystyle \frac{1}{6}}x-{\displaystyle \frac{7}{6}}$

2. 1. ${(f\circ g)}^{-1}(x)={\displaystyle \frac{1}{6}}x-{\displaystyle \frac{7}{6}}=(g^{-1}\circ f^{-1})(x)$

   2. ${(g\circ f)}^{-1}(x)={\displaystyle \frac{1}{6}}x-{\displaystyle \frac{1}{6}}=(f^{-1}\circ g^{-1})(x)$