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3 years ago

Find the inverse of the given function

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

3 0

Answer:

f^-1(x) = 4x^2 -3 . . . . x ≤ 0

Step-by-step explanation:

Interchange x and y, then solve for y.

x = -1/2√(y+3)

-2x = √(y +3)

4x^2 = y +3

4x^2 -3 = y

Note that the range of the function f(x) is f(x) ≤ 0, so this will be the domain of the inverse function. Then the inverse function is ...

f^-1(x) = 4x^2 -3 . . . . for x ≤ 0

___

The attached graph shows this inverse function is a reflection of the function across the line y=x, as it should be.

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The initial cost of an office fax machine is $100. After 1 year, its value becomes $80. Which is the correct linear depreciation

Elis [28]

Answer:

$y=100-20x$

Step-by-step explanation:

Let the x-axis be the time (in years) and the y-axis the value of the fax machine (in dollars).

We know that the initial value of the fax machine is $100; in other words, when the time is zero years, the value is $100, or as an ordered pair (0, 100). We also know that after 1 year the value decreases to $80, so (1, 80).

Now we can find the slope of the line passing through those two points using the slope formula

$m=\frac{y_2-y_1}{x_2-x_1}$

where

$m$ is the slope

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

Replacing values:

$m=\frac{80-100}{1-0}$

$m=-20$

Now, to complete our model we are using the point slope formula

$y-y_1=m(x-x_1)$

where

$m$ is the slope

$(x_1,y_1)$ are the coordinates of the first point

Replacing values:

$y-100=-20(x-0)$

$y-100=-20x$

$y=-20x+100$

$y=100-20x$

We can conclude that the correct linear depreciation model is $y=100-20x$

7 0

3 years ago

AREA OF CIRCLES PLS HELPP

Ksju [112]

Answer:

r = 3 ft

Step-by-step explanation:

A = πr²

9π = πr²

9π/π = r²

9 = r²

√9 = r

3 = r

Hope this helps!

7 0

3 years ago

Urgent help please!!!!!!!! Need the answer...

meriva

Answer:

Step-by-step explanation:

540 is the sum of all angles in a pentagon

The ANGLE STP is 180-50 = 130

540 - 130 is 410

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4 years ago

following frequency distribution shows the daily expenditure on milk of 30 households in a locality:Daily expenditure on milk(in

valina [46]

Note: As you missed to identify what we have to find in this question. But, after a little research, I am able to find that we had to find the Mode for the data given in your question. So, I am assuming we have to calculate the the Mode. Hopefully, it would clear your concept regarding this topic.

Answer:

The mode of the data = 75

Step-by-step explanation:

Lets visualize the given data in a table to show the frequency distribution:

Daily expenditure on milk (in Rs) Number of households

0-30 5

30-60 6

60-90 9

90-120 6

120-150 4

Here the maximum frequency is 9.

So, modal class is 60-90.