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Anuta_ua [19.1K]
3 years ago
8

If f(x) = 7 + 4x and g(x)=1/2x, what is the value of (f/g)(5)?

Mathematics
2 answers:
sineoko [7]3 years ago
5 0

Answer:

The correct option is d.

Step-by-step explanation:

The given functions are

f(x)=7+4x

g(x)=\frac{1}{2x}

Substitute x=5 in each function.

f(5)=7+4(5)=7+20=27

g(5)=\frac{1}{2(5)}=\frac{1}{10}

We need to find the value of (f/g)(5).

(\frac{f}{g})(5)=\frac{f(5)}{g(5)}

Substitute f(5)=27 and g(5)=\frac{1}{10} in the above equation.

(\frac{f}{g})(5)=\frac{27}{\frac{1}{10}}

(\frac{f}{g})(5)=27\times 10=270

The value of  (f/g)(5) is 270. Therefore the correct option is d.

Romashka [77]3 years ago
3 0
<h2>Answer:</h2>

d. \ \boxed{270}

<h2>Step-by-step explanation:</h2>

In this exercise we need to make a division and evaluate the new function at x=5. so we have two functions, namely:

f(x)=7+4x \ and \\ \\ g(x)=\frac{1}{2x}  

Therefore:

f(5)=7+4(5)=27 \\ \\ g(5)=\frac{1}{2\times 5}=\frac{1}{10}

So:

(f/g)(5)=\frac{27}{\frac{1}{10}}=270

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2 years ago
For the function g(x)=3-8(1/4)^2-x
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Using function concepts, it is found that:

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------------------------------------

The given function is:

g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}

------------------------------------

Question a:

The y-intercept is g(0), thus:

g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5

The y-intercept is y = 2.5.

------------------------------------

Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3

--------------------------------------------------

\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty

Thus, the horizontal asymptote is x = 3.

--------------------------------------------------

Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

--------------------------------------------------

Question d:

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--------------------------------------------------

The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631

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