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V125BC [204]
3 years ago
7

If f(x)=x+7 and g(x)= 1 divided by x-13, what is the domain of (f•g)(x)?

Mathematics
1 answer:
andrew11 [14]3 years ago
5 0
<h2>Hello!</h2>

The answer is:

The domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

<h2>Why?</h2>

This is a composite function problem. To solve it, we need to remember how to composite a function. Composing a function consists of evaluating a function into another function.

Composite function is equal to:

f(g(x))=(f\circ} g)(x)

So, the given functions are:

f(x)=x+7\\\\g(x)=\frac{1}{x-13}

Then, composing the functions, we have:

f(g(x))=\frac{1}{x-13}+7\\

Therefore, we must remember that the domain are all those possible inputs where the function can exists, most of the functions can exists along the real numbers with no rectrictions, however, for this case, there is a restriction that must be applied to the resultant composite function.

If we evaluate "x" equal to 13, the denominator will tend to 0, and create an indetermination since there is no result in the real numbers for a real number divided by 0.

So, the domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

Have a nice day!

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Answer:

p, m, n.

Step-by-step explanation:

It is given that,

n=p(m)

Here, p is the name of the function and its variable is m which is independent.

Independent variable : Whose value does not depend on another variable.

Dependent variable : whose value depends on the another variable.

Since the value of n depends on the value of p(m) which is a function of m, therefore n is a dependent variable which depends on the variable m.

∴ If n = p(m), p is the function name, m is the independent variable,  and n is the dependent variable.

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3 years ago
Mr. Logan agrees to give you a loan of 25,000 to start your business, but charge you 7% interest. How much will you have to pay
Hitman42 [59]

Answer:

26000

Step-by-step explanation:

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2 years ago
I only need help with #10 :) offering 10 pts
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Answer:

The length of one side of the square is 3.

Step-by-step explanation:

The perimeter of any given shape is all of the sides added together. So, the perimeter of the triangle is 5x + 4x + 3x. Added together, 12x.

The perimeter of the square is (x + 2)*4. Distributed, it's 4x + 8. Since we know they're equal, set it up like this:

12x = 4x + 8

You then find that x = 1. Plug that into one side of the square, x + 2, to get 3.

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3 years ago
The points (-7,-1) and (-8,6) fall on a particular line. What is its equation in point-slope form?
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Answer:

y - 6 = -7(x + 8)

Step-by-step explanation:

Slope: m = (y2-y1)/(x2-x1) = (6 - -1)/(-8 - -7) = (6 + 1)/(-8 + 7) = 7/-1 = -7

Point-slope form: y - 6 = -7(x - -8)

=> y - 6 = -7(x + 8)

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2 years ago
What is an equation of the line that passes through the points (0, -4)(0,−4) and (-4, 6)(−4,6)
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Answer:

m= 6-(-4)/-4-0 = -5/2

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Step-by-step explanation:

Use the formula m=y2-y1/x2-x1

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2 years ago
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