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yawa3891 [41]
3 years ago
10

Determine the domain of the function (f o g)(x) where f(x)= 3/x+2 and g=5/x.

Mathematics
1 answer:
vitfil [10]3 years ago
7 0

Answer:

The Domain is all real values of x except x = 0 and x = -2.5.

Step-by-step explanation:

I am assuming that f(x) = 3/(x + 2).

(f o g)x is found by substituting  5/x for the x in 3/(x + 2).

(f o g) x = 3/ ( 5/x + 2)

= 3 / ( 5+2x) / x

= 3x / (5 + 2x).

When finding the domain you  first check for values of x which make g(x) undefined then values of x which make (f o g)(x) undefined.

x = 0 makes  g(x) = 5/0 so it is undefined and  x = -2.5 makes g o f undefined also.

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Answer:

<u><em>Part A:</em></u> D. y = (x + 1)(x+3)\\

<u><em>Part B:</em></u> C. 3x(x-3) = 0\\

Step-by-step explanation:

For part A) we just have to plug in 0 for x and solve for y until we find the equation that says 3 is the value for y when x is 0. For purposes of speeding up the process the correct answer is D. I will show how to check for it now.

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Now plug in 0 for x.

y = (0 + 1)(0+3)\\

Now solve.

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This proves that this is the correct answer.

For part B) we just have to plug in the give values for x separately and check for each value of x that it equals 0. For the purpose of speeding up the process the correct answer is C. I will show how to check for it now.

The equation: 3x(x-3) = 0

Now plug in x for 0 and solve:

3* 0 (0-3) = 0\\

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This equation is true, now we check for the other value of x, 3.

3*3(3-3) = 0\\

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9514 1404 393

Answer:

  (2/3)(e^t +1)^(3/2)

Step-by-step explanation:

Use the substitution ...

  u = e^t +1

Then du = e^t and you are finding the integral of ...

  ∫u^(1/2)·du

which you know by the power rule is ...

  (2/3)u^(3/2) = (2/3)(e^t +1)^(3/2)

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