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4 years ago

Find ( f o g) (x) when f (x) = x^2+6x+5 and g(x)=1/x+1

Mathematics

1 answer:

olchik [2.2K]4 years ago

7 0

Answer:

$(f\circ g)(x)=\frac{1}{x^{2}}+\frac{8}{x}+12$

Step-by-step explanation:

Given that $f (x) = x^{2}+6x+5$ and $g(x)=\frac{1}{x}+1$ are the functions.

To find $(f\circ g)(x)$ with the given two functions. ie., to find the composite function of f(x) and g(x) which is denoted by $(f\circ g)(x)$

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

$=f(\frac{1}{x}+1)$

$=({\frac{1}{x}+1})^{2}+6\times ({\frac{1}{x}+1})+5$

$=\frac{1}{x^{2}}+\frac{2}{x}+1+\frac{6}{x}+6+5$

$=\frac{1}{x^{2}}+\frac{8}{x}+12$

Therefore $(f\circ g)(x)=\frac{1}{x^{2}}+\frac{8}{x}+12$

Therefore the composite function of f(x) and g(x) is $(f\circ g)(x)=\frac{1}{x^{2}}+\frac{8}{x}+12$

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Does a parallelogram have to have equal sides

Rudik [331]

Answer:

The two shorter sides have to be equal and the two longer sides have to be equal.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Which of the following choices is the standard deviation of the sample shown

lana66690 [7]

Answer: E. square root of 2

We can write that in shorthand as sqrt(2)

sqrt(2) = 1.41421 approximately

======================================================

Explanation:

Step 1)

Add up the values to get 18+19+20+21+22 = 100

Divide by n = 5, since there are 5 items in the list. So 100/n = 100/5 = 20

The sample mean is xbar = 20

--------------

Step 2)

Subtract the mean from each data value

18 - xbar = 18 - 20 = -2
19 - xbar = 19 - 20 = -1
20 - xbar = 20 - 20 = 0
21 - xbar = 21 - 20 = 1
22 - xbar = 22 - 20 = 2

The results we get are: -2, -1, 0, 1, 2

---------------

Step 3)

Square the results from the previous step

(-2)^2 = 4
(-1)^2 = 1
(0)^2 = 0
(1)^2 = 1
(2)^2 = 4

The results here are: 4, 1, 0, 1, 4

---------------

Step 4)

Add up those squares from the previous step: 4+1+0+1+4 = 10

Now divide by n = 5 to get 10/n = 10/5 = 2

The result 2 represents the population variance. Applying the square root to the population variance leads to the population standard deviation. So we end up with the final answer of sqrt(2). The answer is choice E.

sqrt(2) = 1.41421 approximately

---------------

Note: if you want the sample standard deviation, then you divide by n-1 = 5-1 = 4, but the other steps are the same as before.

7 0

3 years ago

Yuri makes $8.00 an hour, plus 3% commission on sales. If he works for 30 hours and sells $4,600 worth of merchandise, how much

horrorfan [7]

Answer:

4,847.2

Step-by-step explanation:

$8×30=$240

$240+3%=247.2

$4,600+247.2=4,847.2

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3 years ago

Read 2 more answers

Write three functions. In the first function, y should vary directly with x. In the second function, y should vary inversely wit

skelet666 [1.2K]

A) First function, y varies directly with x.

1) function: y = (3/4)x

2) graph: it is a straight line that passes through the origin and has slope 3/4. The slope means that the rate of change of the function is 3 units per every 4 units the x-value incresase or, what is the same 0.75 units per incresase unit of x - value.

3) real world example

A recipe of a cake instructs to use 3 cups of sugar for every 4 cups of flour. So, how much flour you need if you have 12 cups of sugar?

y = (3/4)x , so if x = 3, y = (3/4)*12 = 3*12/4 = 9.

So, given that the variation is direct you multiply the number of cups of sugar times the constant rate, 3/4, to get the number of cups of flour in relation with the given amount of sugar.

B) The second function: y varies inversely with x.

Inverse variation => y*x = constant or y = constant / x.

Tnat means that if x increase y will decrease in the same factor that x increases.

1) function: y = 12 / x

2) graph: the form of this graph is called hyperbola, it is a decreasing line from left to right. It has two asymptotes, the y-axis (x =0) and the x-axis (y = 0). That means that x and y can never be zero.

As the x-value approaches 0, the y value approaches positive or negative infinity; as the y-values approaches 0 the x-values approaches to positive or negative infinity.

If you take the positive values, the graph is a decreasing curve in the first quadrant (x and y are positive).

If you take the negative values, the graphs is a decreasing curve in the third quadrant (x and y are negative)

3) real world example.

The relatioship between velocity and time in a uniform motion.

If the distance run by an object is constant, as the velocity increases the time decreases in the same factor.

Suppse a distant of 100 km between cities A and B.

How long will it take to travel from A to B at 50 km/ h and 25 km/h ?:

100 km = velocity * time

at 50 km/h: 100 km = 50 km/h * t => t = [100 km ] / [50 km/h] = 2 hours

at 25 km/h: 100 kg = 25 km/h * t => t = [ 100 km ] / [25 km/h] = 4 hours.

C) Third case, the relationship between x and y should is neither inverse variation nor direct variation.

Of course, there are infinite type of functions that are neither inverse variation nor direct variation: linear (that do not passe through the origin), quadratic, exponential, logarithmical, trigonometric sine, ...

1) example of function: y = 30 + 2x

2) graph: it is a straigh line with y-intercept 30 and slope 2.

3) real world example:

The cost of producing chairs consists of 30 dollars of rent for the facility plus 2 dollar to produce each chair, so the total cost y is 30 + 2x.

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4 years ago

How long will it take for an investment to triple, if interest is compounded continuously at 8%?

maw [93]

Answer:

It will take 14 years before the investment triples

Step-by-step explanation:

Continuous Compounding

Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.

The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:

$FV = PV\cdot e^{i.t}$