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Bogdan [553]
4 years ago
15

The function g(x) =x^(2)+3. The function f(x)=g(x+2).

Mathematics
2 answers:
Tpy6a [65]4 years ago
6 0

Answer:2 units left of g(x)

2 units down from g(x)

Step-by-step explanation: plug in the formulas

r-ruslan [8.4K]4 years ago
6 0

Answer:

Function is shifted horizontally, 2 units left of g(x). There is no vertical shift.

Step-by-step explanation:

Adding a real number s to the argument of a function will have an effect of shifting the graph of the function horizontally by s units. If s>0 the shift is to the left, for s<0 the shift is to the right. See attached plot of the two functions  of g(x) and g(x+2), if you are curious enough.  

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Please find the derivative of <img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Be%5E%7B%5Cfrac%7B3%7D%7Bx%7D%7D%7D%7
sesenic [268]

Hello! :)

\large\boxed{\frac{-e^{\frac{3}{x}}  (3 + 2x )}{x^{4}}}

Find the derivative using the quotient rule:

\frac{f(x)}{g(x)} = \frac{g(x) * f'(x) - f(x) * g'(x)}{(g(x))^{2}}

In this instance:

f(x) = e^{\frac{3}{x} }\\\\g(x) = x^{2}

Use the following properties to find the derivative of f(x) and g(x):

e^{u} = u' * e^{u}\\\\x^{n} = nx^{n-1}

Use the quotient rule:

\frac{x^{2} * (e^{\frac{3}{x}} * (-3x^{-2})) - e^{\frac{3}{x}} * 2x  }{(x^{2} )^{2}}

Simplify the numerator:

\frac{(e^{\frac{3}{x}} * (-3)) - e^{\frac{3}{x}} * 2x  }{(x^{2} )^{2}}

Factor out e^{\frac{3}{x}}

\frac{e^{\frac{3}{x}}  (-3 - 2x )}{x^{4}}

Factor out -1 from the numerator:

\frac{-e^{\frac{3}{x}}  (3 + 2x )}{x^{4}}

And we're done! Thanks for posting the question to my 1000th answer!

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Answer:

A. 3

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Let the integers be

x

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