Answered

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

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



Answer :

GinnyAnswer
First, we need to determine the values of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] at [tex]\( x = 5 \)[/tex].

1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 5 \)[/tex]:

Given [tex]\( f(x) = 7 + 4x \)[/tex],

[tex]\[ f(5) = 7 + 4(5) \][/tex]

Calculate the value inside the parentheses:

[tex]\[ 4(5) = 20 \][/tex]

Then add 7:

[tex]\[ f(5) = 7 + 20 = 27 \][/tex]

So, [tex]\( f(5) = 27 \)[/tex].

2. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 5 \)[/tex]:

Given [tex]\( g(x) = \frac{1}{2x} \)[/tex],

[tex]\[ g(5) = \frac{1}{2(5)} \][/tex]

Calculate the value inside the parentheses:

[tex]\[ 2(5) = 10 \][/tex]

Then find the value of the fraction:

[tex]\[ g(5) = \frac{1}{10} = 0.1 \][/tex]

So, [tex]\( g(5) = 0.1 \)[/tex].

3. Calculate [tex]\( \left( \frac{f}{g} \right)(5) \)[/tex]:

To find [tex]\( \left( \frac{f}{g} \right)(5) \)[/tex], we must divide [tex]\( f(5) \)[/tex] by [tex]\( g(5) \)[/tex]:

[tex]\[ \left( \frac{f}{g} \right)(5) = \frac{f(5)}{g(5)} \][/tex]

Substitute [tex]\( f(5) \)[/tex] and [tex]\( g(5) \)[/tex] into the equation:

[tex]\[ \left( \frac{f}{g} \right)(5) = \frac{27}{0.1} \][/tex]

Simplify the fraction:

[tex]\[ \frac{27}{0.1} = 27 \div 0.1 = 270 \][/tex]

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

Thus, the correct answer is [tex]\( 270 \)[/tex].

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