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]
