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BlackZzzverrR [31]
3 years ago
5

If f(x) = x-1/3 and g(x)= 3x+1, what is (f o g)(x)?

Mathematics
1 answer:
N76 [4]3 years ago
6 0

Answer:

(f o g)(x) = 3x + \frac{2}{3}

Step-by-step explanation:

We have the function f(x) = x-\frac{1}{3} and we have the function g(x) = 3x + 1. We want to find g(x) composed with f(x)

Then, the function (f o g)(x) is the same since f(g(x))

That is, you must do x = g(x) and then enter g(x) into the function f(x).

f(g(x)) = (g(x)) -\frac{1}{3}

f(g(x)) = (3x + 1) -\frac{1}{3}

Simplifying, we obtain:

(f o g)(x) = 3x + 1 -\frac{1}{3}\\\\(f o g)(x) = 3x + \frac{2}{3}

Finally. The composite function is:

(f o g)(x) = 3x + \frac{2}{3}

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Circle Q is centered at the origin with radius r. Point P(x, y) lies on circle Q. Make a conjecture. How can you find an equatio
salantis [7]

Answer:

The relation x^{2} +y^{2} =r^{2} is explained below.

Step-by-step explanation:

P(x, y) is a point on the circle. Q is the origin. Join PQ.

PQ is the radius.

Therefore, PQ = r

Draw PS perpendicular to the x-axis.

Now, ΔPQS is a right triangle.

By Pythagoros theorem,

PQ^{2}=PS^{2} +QS^{2}

r^{2}=x^{2} +y^{2}

x^{2} +y^{2} =r^{2}

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URGENT HELP NEEDED
kondor19780726 [428]
<span>"ratio of princesses to celebrities is 3:1"

The are 3 more times princesses as celebrities.

</span>"<span>The ratio of superheros to princesses is 5:4"

For each 4 princesses, there are 5 superheroes.

For 1 celebrity, there are 3 pincesses.

For 4 celebrities, there are 12 princesses.
For 12 princesses, there are 15 superheroes.

The ratio of celebrities to princesses to superheroes is
4:12:15 or 4x:12x:15x

Add them: 4x + 12x + 15x = 31x

31x = 93

x = 93/31 = 3

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Superheroes: 15x = 15(3) = 45

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3 years ago
The constant of proportionality of chicken nuggets in relation
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I beleive that it would be C=n25

Step-by-step explanation:

I'm not sure if this is not complex enough but I'm just going by what I think this is.

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The mean one-way commute to work in Chowchilla is 7 minutes. The standard deviation is 2.4 minutes, and the population is normal
adell [148]

Answer:

The answer is below

Step-by-step explanation:

Given that:

The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z=\frac{x-\mu}{\sigma}

a) For x < 2:

z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08

From normal distribution table,  P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%

b) For x = 2:

z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08

For x = 11:

z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67

From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337  

c) For x = 11:

z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67

From normal distribution table,  P(x < 11) = P(z < 1.67) = 0.9525

d) For x = 2:

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z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83

From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) =  0.2033- 0.0188 = 0.1845  

e) For x = 5:

z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83

From normal distribution table,  P(x < 5) = P(z < -0.83) = 0.2033

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Step-by-step explanation:

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