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3 years ago

Given f(x) = (-1/7)(sqrt 16-x^2), find f^-1(x). Then state whether the inverse is a function.

Mathematics

1 answer:

Viefleur [7K]3 years ago

8 0

Answer:

f^-1(x) = ±√(16 -49x^2) . . . . -4/7 ≤ x ≤ 0
not a function

Step-by-step explanation:

The usual method of finding the inverse of a function is to solve for y the equation ...

x = f(y)

The inverse is only defined on the range of the original function, so for ...

0 ≥ x ≥ -4/7

Here, that looks like ...

x = (-1/7)√(16 -y^2)

-7x = √(16 -y^2) . . . multiply by -7

49x^2 = 16 -y^2 . . . square both sides

y^2 + 49x^2 = 16 . . . add y^2

y^2 = 16 -49x^2 . . . . subtract 49x^2

y = ±√(16 -49x^2) . . . . take the square root

So, the inverse function is ...

f^-1(x) = ±√(16 -49x^2) . . . . . defined only for -4/7 ≤ x ≤ 0

This gives two output values for each input value, so is not a function.

_____

The original f(x) is the bottom half of an ellipse, so does not pass the horizontal line test. It cannot have an inverse function.

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The ratio of two numbers is 4:5 if the larger number is 300 what is the smaller number

yaroslaw [1]

Answer:

The smaller number is 240.

Step-by-step explanation:

The question says that the larger number is 300, so 5 has to be 300.

4:5

?:300

You can use cross-multiplication or find the scale factor to find the answer.

Cross-multiplication:

4 × 300 ÷ 5 = 240

Finding the scale factor:

300 ÷ 5 = 60

4 × 60 = 240

The smaller number is 240.

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2 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

ddd [48]

Answer:

$f'(x) = 4x^2 - 3$ for $x \le -3$

Step-by-step explanation:

See attachment for proper question

Given

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

For

$x \ge -3$

Required

Determine the inverse function

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

Replace f(x) with y

$y = -\frac{1}{2}\sqrt{x + 3}$

Swap the positions of x and y

$x = -\frac{1}{2}\sqrt{y + 3}$

Multiply both sides by -2

$-2 * x =-2 * -\frac{1}{2}\sqrt{y + 3}$

$-2x =\sqrt{y + 3}$

Square both sides

$(-2x)^2 =(\sqrt{y + 3})^2$

$4x^2 =y + 3$

Make y the subject

$y = 4x^2 - 3$

The inverse has been solved. So, we need to replace y with f'(x)

$f'(x) = 4x^2 - 3$

Next, is to determine the interval

$x \ge -3$

Change inequality to $\le$

$x \le -3$

Hence, the inverse function is:

$f'(x) = 4x^2 - 3$ for $x \le -3$

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2 years ago

Can 57 rows be divided into equal sections

Serjik [45]

Yes it can be divided into 3 equal sections of 19

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3 years ago

Read 2 more answers

Anyone know this ???...

Karolina [17]

Answer:

4250 children

Step-by-step explanation:

72-38=34 degrees

34 degrees therefore is 578 people

so, 1 degree is 17 people

There is 360 degrees in a circle so we must subtract the degrees of the men and female segments in order to know how many degrees children takes up:

360-72-38=250

250x17=4250 children

3 0

2 years ago

Heidikae reads 420 pages a week. In the summer, she reads 17% less. Approximately how many pages per week does she read in the s

Marat540 [252]

420-17%= 348.6

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3 years ago