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3 years ago

I really need help, it won't take long to solve (:

Mathematics

1 answer:

stira [4]3 years ago

5 0

47. x^2-5x+6 = (x-3)(x-2) = 0
x = 3, 2
B

48. xy = 0
Then x or y must equal 0
D

49. Plug in each of the answer choices to see if they work.
B

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For which function is f(x) equal to f^1(x) ( answer choices in picture )

Sonja [21]

Answer:

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

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

$f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+6}{y-6}$

Rewrite in terms of 'y'. This gives,

$x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}$

The given function $y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}$

So, option A is incorrect.

Option B:

$f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+2}{y-2}$

Rewrite in terms of 'y'. This gives,

$x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}$

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

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

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

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

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+5}{y-5}$

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

The given function $y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}$

So, option D is incorrect.

Therefore, only option C is correct.

7 0

3 years ago

Raquel and Van live in two different cities. As part of a project, they each record the lowest prices for a gallon of gas at gas

jeyben [28]

Answer:

Step-by-step explanation:

Looking at the information given, the average or mean lowest prices and standard deviations for the two cities are given. The standard deviation is a measure of variability. It is used to determine how far the values in the data are from the mean. A lower standard deviation means that the values are closer to the mean. A higher standard deviation means that the values are farther from the mean.

Since 0.07 is lower than 0.23, the correct statement that is true about their gas-price data is

Raquel's data are most likely closer to $3.42 than Van's data are to $3.78.

3 0

3 years ago

Read 2 more answers

7 cm<br> 4 cm<br> 8 cm<br> what is the area?

adell [148]

what shape is this

I cant answer it if there's no shape in the question

5 0

3 years ago

Read 2 more answers

12ft 6ft 6ft 6ft what is the area of this face

Ainat [17]

Answer:

2,592ft

Step-by-step explanation:

The answer is 2,592ft because I multiplied 12ftX6ftX 6ftX6ft=2,952ft .

7 0

3 years ago

What is the equivalent ratio to the ratio 4:6.how do I know the ratio is equivalent?

zimovet [89]

Since you asked, simply, to know how a ratio is equivalent to another.

Ratios are like fractions in the way that they can be multiplied and simplified. 1:2, for example, can also be 10:20, 5:10, etc. This is inherent to the way a ratio works - say, for every 1 person, there are two cheese slices. This means that when the group gets larger, so does the amount of cheese slices.

Now, to find an equivalent ratio. You can simplify 4:6 by finding the GCF (greatest common factor) of these two numbers - something you can divide both of them by evenly. In this case, the GCF is 2. We divide both 'sides' by 2, and we get a simplified ratio of 2:3. You can then multiply this by different numbers (ones that are logical and could reasonably lead you to an answer on your worksheet or whatnot) until you find an equivalent ratio.

8 0

3 years ago