Practice Problems

Work through the odd-numbered problems 1-31. Once you have completed the problem set, check your answers.

Answers

(c) If $T= 11oC$ , $WCI = \left\{ \begin{array} {ll}11 & \text { if } 0 ≤ v ≤ 6.5 \\33 - \dfrac{10.45+5.29\sqrt v - 0.279v}{22} (22) & \text { if } 6.5 ≤ v ≤ 72 \\ -2.2 & \text { if } 72 < v \end{array} \right.$

3. $g(0)=3$ , $g(1)=1$ , $g(2)=2$ , $g(3)=3$ , $g(4)=1$ , $g(5)=1$ . $g(x)= \left\{ \begin{array} {lll} 3 - x & \text { if } x < 1 \\ x & \text { if } 1 ≤ x ≤ 3 \\ 1 & \text { if } x > 3 \end{array} \right.$

5.

(a) $f( f(1) ) = 1$ , $f( g(2) ) = 2$ , $f( g(0) ) = 2$ , $f( g(1) ) = 3$
(b) $g( f(2) ) = 0$ , $g( f(3) ) = 1$ , $g( g(0) ) = 0$ , $g( f(0) ) = 0$
(c) $f (h(3) ) = 3$ , $f( h(4) ) = 2$ , $h( g(0) ) = 0$ , $h( g(1) ) = –1$

7. (a)


$x$	-1	0	1	2	3	4
$f(x)$	3	3	-1	0	1	1
$g(x)$	-2	0	1	2	3	4
$h(x)$	-3	-2	-1	0	1	2

(b)

$f( g(1) ) = –1$ ,

$f( h(1) ) = 3$ ,

$h( f(1) ) = –3$ ,

$f( f(2) ) = 3$ ,

$g( g(3.5) ) = 3$

(c) See Fig. 0.4P7 for the graphs of

$f$ ,

$g$ , and

$h$ .

$L(d) = \left\{ \begin{array} {llll} England & \text { if d = Mon. or Tue. } 0 ≤ v ≤ 6.5 \\ France & \text { if d = Wed.} 6.5 ≤ v ≤ 72 \\ Germany & \text { if d = Thur. or Fri.} 72 < v \\ Italy & \text { if d = Sat. or Sun.} \end{array} \right.$

11. $f(x)= \left\{ \begin{array} {ll} x^2 & \text { if } x< 2 \\ x - 1 & \text { if } x > 2 \end{array} \right.$

13. (a) $B(1) = 1.f(1) = 1. \dfrac{1}{1} = 1$ ,
$B(2) = 2.f(2) = 2. \dfrac{1}{2} = 1$ ,
$B(3) = 3.f(3) = 3. \dfrac{1}{3} = 1$ .