Answer
(a) 265 mi (b) 1084588 miles
Work Step by Step
(a) As we know 1 ft = 12 inches
This implies
2 ft = 24 inches
$f(24)=(24)^{2} =576$ inches
This implies $f(24)=\frac{576}{12}$ ft $=48$ ft
As per statement, $g(x)=2^{x}=g(24)=2^{24}$inches
Hence, $g(24)=2^{24}$inches
Since, $1$ mile $=5280$ ft
Thus, $g(24)=\frac{2^{24}}{12\times 5280}=265$ mi
(b) Since 3 ft = 36 inches
Thus, $log_{2}x=36$
Using formula $log_{b}x=y=b^{y}=x$
This implies $x=2^{36}$ inches
Hence, $x= \frac{2^{36}}{12\times 5280}\approx 1084588$ miles
