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horsena [70]
3 years ago
8

For the real valued functions f(x) = x-4/x-5 and g(x) = 4x+17, find the composition fog and specify its domain using interval no

tation.
(F o g)(x)=
Domain of f o g:

Mathematics
1 answer:
Studentka2010 [4]3 years ago
3 0

Answer:

(f o g)(x) = \frac{4x+13}{4x+12}

Domain : (-∞, -3) ∪ (-3, ∞)

Step-by-step explanation:

Given : f(x) = \frac{x-4}{x-5}

            g(x) = 4x + 17

We have to find the value of (f o g)(x).

Since (f o g)(x) = f[g(x)]

                        = \frac{(4x+17)-4}{(4x+17)-5}

                        = \frac{4x+13}{4x+12}

For the Domain of the function (f o g)(x),

Given function is defined for (4x + 12) ≠ 0

4x ≠ -12

x ≠ -3

Therefore, Domain of the function will be : (-∞, -3) ∪ (-3, ∞)                    

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A high school class consists of 5 ​seniors, 10 ​juniors, 13 ​sophomores, and 4 freshmen. Exactly 4 of the juniors are male​, and
lozanna [386]

Answer:

The probability that the pair consists of a female junior and a male sophomore is 0.096

Step-by-step explanation:

No of male juniors=4

No of female juniors=10-4=6

No of female sophomores=5

No of male sophomores=13-5=8

As per question,

Probability that the pair consists of a female junior and

a male sophomore =\frac{6C1\times8C1}{32C2}=0.096

Therefore, the probability that the pair consists of a female junior and a male sophomore is 0.096

7 0
3 years ago
GUYS PLEASE HELP ME HELP HELP PLEASE PLEASE!!! Simplify and solve for the unknown. Use order of operations as needed. Check your
grandymaker [24]

The solution is B = 43

Step-by-step explanation:

Simplify and solve for the unknown for 5(B + 3) = 4(B - 7) + 2B

  • Simplify each side
  • Add the like terms in each side if need
  • Separate the unknown in one side and the numerical term in the other side to find the value of the unknown

∵ 5(B + 3) = 4(B - 7) + 2B

- Multiply the bracket (B + 3) by 5 in the left hand side and multiply

  the bracket (B - 7) by 4 in the right hand side

∵ 5(B + 3 ) = 5(B) + 5(3) = 5B + 15

∵ 4(B - 7) = 4(B) - 4(7) = 4B - 28

∴ 5B + 15 = 4B - 28 + 2B

- Add the like terms in the right hand side

∵ 4B + 2B = 6B

∴ 5B + 15 = 6B - 28

- Add 28 to both sides

∴ 5B + 43 = 6B

- Subtract 5B from both sides

∴ 43 = B

- Switch the two sides

∴ B = 43

To check the answer substitute the value of B in each side if the two sides are equal then the solution is right

The left hand side

∵ 5(43 + 3) = 5(46) = 230

The right hand side

∵ 4(43 - 7) + 2(43) = 4(36) + 86 = 144 + 86 = 230

∴ L.H.S = R.H.S

∴ The solution B = 43 is right

The solution is B = 43

Learn more:

You can learn more about the solution of an equation in brainly.com/question/11229113

#LearnwithBrainly

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Answer:

19 dollars per student

Step-by-step explanation:

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