#### Answer

a) $\$18$; b) $x=64$ minutes; c) $x=173$ minutes; d) $[0,43200]$

#### Work Step by Step

We are given:
$C(x)=0.26x+5$
a) Compute $C(50)$:
$C(50)=0.26(50)+5$
$C(50)=18$
b) Solve the equation:
$0.26x+5=21.64$
$0.26x+5-5=21.64-5$
$0.26x=16.64$
$x=\dfrac{16.64}{0.26}$
$x=64$ minutes
c) Solve the inequality $C(x)\leq 50$
$0.26x+5\leq 50$
$0.26x+5-5\leq 50-5$
$0.26x\leq 45$
$x\leq\dfrac{45}{0.26}$
$x\leq 173.08$
$x=173$ minutes
d) The implied domain of $C$ has the minimum 0 (when no calls are made) and the number of minutes in a month (if all minutes in a month are used):
$[0,30\times 24\times 60]=[0,43200]$