If [tex][tex]$f(x) = 7 + 4x$[/tex][/tex] and [tex]$g(x) = \frac{1}{2x}$[/tex], what is the value of [tex]\left(\frac{f}{g}\right)(5)[tex]$[/tex]?

A. $[/tex]\frac{11}{2}[tex]$
B. $[/tex]\frac{27}{10}$
C. 160
D. 270



Answer :

To determine the value of [tex]\(\left(\frac{f}{g}\right)(5)\)[/tex] given the functions [tex]\( f(x) = 7 + 4x \)[/tex] and [tex]\( g(x) = \frac{1}{2x} \)[/tex], we will follow these steps:

1. Calculate [tex]\( f(5) \)[/tex]:
[tex]\[ f(x) = 7 + 4x \][/tex]
Evaluate at [tex]\( x = 5 \)[/tex]:
[tex]\[ f(5) = 7 + 4(5) = 7 + 20 = 27 \][/tex]

2. Calculate [tex]\( g(5) \)[/tex]:
[tex]\[ g(x) = \frac{1}{2x} \][/tex]
Evaluate at [tex]\( x = 5 \)[/tex]:
[tex]\[ g(5) = \frac{1}{2(5)} = \frac{1}{10} = 0.1 \][/tex]

3. Evaluate [tex]\( \left(\frac{f}{g}\right)(5) \)[/tex]:
[tex]\[ \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} \][/tex]
Evaluate at [tex]\( x = 5 \)[/tex]:
[tex]\[ \left(\frac{f}{g}\right)(5) = \frac{f(5)}{g(5)} = \frac{27}{0.1} = 270 \][/tex]

Therefore, the value of [tex]\( \left(\frac{f}{g}\right)(5) \)[/tex] is:
[tex]\[ \boxed{270} \][/tex]