Solutions to Try Its

1. $h\left(2\right)=6$

2. Yes

3. Yes

4. The domain of function ${f}^{-1}$ is $\left(-\infty \text{,}-2\right)$ and the range of function ${f}^{-1}$ is $\left(1,\infty \right)$.

5. a. $f\left(60\right)=50$. In 60 minutes, 50 miles are traveled.

b. ${f}^{-1}\left(60\right)=70$. To travel 60 miles, it will take 70 minutes.

6. a. 3; b. 5.6

7. $x=3y+5$

8. ${f}^{-1}\left(x\right)={\left(2-x\right)}^{2};\text{domain}\text{of}f:\left[0,\infty \right);\text{domain}\text{of}{f}^{-1}:\left(-\infty ,2\right]\\$

9.

Solutions to Odd-Numbered Exercises

1. Each output of a function must have exactly one output for the function to be one-to-one. If any horizontal line crosses the graph of a function more than once, that means that $y$ -values repeat and the function is not one-to-one. If no horizontal line crosses the graph of the function more than once, then no $y$ -values repeat and the function is one-to-one.

3. Yes. For example, $f\left(x\right)=\frac{1}{x}\\$ is its own inverse.

5. Given a function $y=f\left(x\right)$, solve for $x$ in terms of $y$. Interchange the $x$ and $y$. Solve the new equation for $y$. The expression for $y$ is the inverse, $y={f}^{-1}\left(x\right)$.

7. ${f}^{-1}\left(x\right)=x - 3$

9. ${f}^{-1}\left(x\right)=2-x$

11. ${f}^{-1}\left(x\right)=\frac{-2x}{x - 1}\\$

13. domain of $f\left(x\right):\left[-7,\infty \right);{f}^{-1}\left(x\right)=\sqrt{x}-7$

15. domain of $f\left(x\right):\left[0,\infty \right);{f}^{-1}\left(x\right)=\sqrt{x+5}\\$

17. $f\left(g\left(x\right)\right)=x,g\left(f\left(x\right)\right)=x$

19. one-to-one

21. one-to-one

23. not one-to-one

25. $3$

27. $2$

29.

31. $\left[2,10\right]$

33. $6$

35. $-4$

37. $0$

39. $1$

41.

43. ${f}^{-1}\left(x\right)={\left(1+x\right)}^{1/3}\\$

45. ${f}^{-1}\left(x\right)=\frac{5}{9}\left(x - 32\right)\\$. Given the Fahrenheit temperature, $x$, this formula allows you to calculate the Celsius temperature.

47. $t\left(d\right)=\frac{d}{50}\\$, $t\left(180\right)=\frac{180}{50}\\$. The time for the car to travel 180 miles is 3.6 hours.