Please help giving brainliest

Consider the functions f(x) = 2x and g(x) = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-3%7D" id="TexFormula1" title="\

bagirrra123 [75]

Question 1:

For this case we must find $(f_ {0} g) (4)$ knowing that:

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

By definition we have that, be two functions f (x) and g (x), then the composite function of f with g is:

$(g_ {0} f) (x) = g [f (x)]$

In this case, they ask us for the function composed of g with f:

$(f_ {0} g) (x) = f [g (x)]$

So, we have:

$(f_ {0} g) (x) = 2 (\frac {1} {x-3})\\(f_ {0} g) (4) = 2 (\frac {1} {4-3})\\(f_ {0} g) (4) = 1$

ANswer:

$(f_ {0} g) (4) = 1$

Question 2:

For this case, we must find the inverse function of $g (x) = \frac {1} {x-3}$ , given by: $g ^ {- 1} (x)$

To do this, replace g(x) with y:

$y = \frac {1} {x-3}$

We exchange variables:

$x = \frac {1} {y-3}$

We solve for "y":

$y-3 = \frac {1} {x}\\y = \frac {1} {x} +3$

Replace "y" with $g ^ {-1} (x)$

So, we have:

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

Answer:

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

Question 3:

For this case, we have by definition, the domain of a function f (x), is the set of all the values for which the function is defined.

We must find the domain of the following function:

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

It is observed that the function is not defined for $x = 0$

Then the domain is given by all the values of x, except 0.

${x | x \neq 0}$ for any integer n

Answer:

All numbers, except $x = 0$

4 0

3 years ago

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The number of students enrolled at a college is 18,000 and grows 6% each year.

Elis [28]

Answer:

If the question is how many student enroll in the school each year then the answer is 1080

Step-by-step explanation:

3 0

4 years ago

What number is 45% of 5/9

igor_vitrenko [27]

The right answer is 1/4

7 0

3 years ago

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A prism has an volume of 8 yd3. What is its volume in ft3?

Kaylis [27]

8x3=24 ft3 3 feet are in a yard.

3 0

3 years ago

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A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondent

nadya68 [22]

Answer:

$\r p = 0.11$

$\r q = 0.89$

n = 2000

$E = \pm 5$

p - population proportion

$\alpha = 5$ %

Step-by-step explanation:

From the question we are told that

The sample size is $n = 2000$

The proportion of the population for chocolate pie is $p_c = 0.11$

The margin of error is $E = \pm 5$ %

Now in the question we are asked to provide the meaning of

$\r p , \r q , n , E , and\ p$

Now $\r p$ is the sample proportion of the population that those chocolate pie as favorite pie of which is given from the question as 0.11

Now

$\r q$ is the sample proportion of the population that choose other pies apart from chocolate pie as their favorite and it is evaluated as

$\r q = 1 - \r p$

$\r q = 1 - 0.11$

$\r q = 0.89$

n is the sample size which is given as n = 2000

E is the margin of error which given as $E = \pm 5$ %

p is the population proportion

Given that the confidence level is 95 % then the level of significance is mathematically evaluated as

$\alpha =(100 - 95)$ %

$\alpha =$ 5%

4 0

4 years ago