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ryzh [129]
3 years ago
5

Determine the domain of (f/g) (x) when f(x)=1/x and g(x)= sqrt x+5

Mathematics
2 answers:
ra1l [238]3 years ago
7 0

Answer:

all work is answer and shown and pictured

Lena [83]3 years ago
3 0
<h2>Answer:</h2>

The domain is:   {x > -5 and x≠0 }

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

We are given a function f(x) and g(x) as follows:

f(x)=\dfrac{1}{x}

and

g(x)=\sqrt{x+5}

Now, the function (f/g)(x) is given by:

(\dfrac{f}{g})(x)=\dfrac{f(x)}{g(x)}

This means that:

(\dfrac{f}{g})(x)=\dfrac{\dfrac{1}{x}}{\sqrt{x+5}}

i.e.

(\dfrac{f}{g})(x)=\dfrac{1}{x\sqrt{x+5}}

Now we know that a square root function is defined if the radicand is positive.

i.e.

Here,

x+5 ≥ 0

i.e.

x ≥ -5

Also,

x≠0 and √(x+5)≠0

( otherwise the denominator will be zero and hence the expression will be not defined)

Hence, we have:

x≠0 and x≠ -5

This means that:

 x > -5 and x≠0

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3 years ago
Figure below shows two triangles EFG and KLM​
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Answer:

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3 0
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rachel bought one double pack of CDs for $20. this is $4 less than 3/4 the cost of a triple pack of CDs. what is the price of a
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3 years ago
Every year the Lee family has a big family dinner, and everyone brings a mug to exchange. The mugs are put on wooden hangers on
RideAnS [48]

Answer:

21 more mugs were brought this year than last year.

Step-by-step explanation:

We can solve by subtracting the initial amount of mugs from the final amount of mugs.

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4 0
2 years ago
In triangle XYZ, angle Y = 45º and angle Z = 60º. If XZ = 4, then what is XY?
Katena32 [7]

Answer:

XY = 4.9

Step-by-step explanation:

Given

XZ= 4

\angle Y = 45

\angle Z = 60

Required

Determine the measure of side XY

To do this, we make use of sine law. This is as follows:

\frac{a}{\sin\ A} = \frac{b}{\sin\ B} = \frac{c}{\sin\ C}

In this case:

\frac{4}{\sin(45)} = \frac{XY}{\sin(60)}

Cross Multiply

XY * \sin(45) = 4 * \sin(60)

XY * 0.7071 = 4 * 0.8660

Make XY the subject

XY = \frac{4 * 0.8660}{0.7071}

XY = \frac{3.4640}{0.7071}

XY = 4.89888276057

XY = 4.9 -- <em>approximated</em>

3 0
3 years ago
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