Sequence for the numbers 3, -6, 12, 4, 20, ?

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

The numbers 4, 5, 6, and 7 are on a spinner. You spin the spinner twice. Which calculation proves that landing on an even number

drek231 [11]

Answer:

C

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

The expression 120-15x represents how many invitations Luanne has to address after x days. The expression 120 + 15(7-x) represen

Aloiza [94]

Answer:

not possible.

Step-by-step explanation:

number of invitations luanne has to address after x days = 120-15x

number of invitations Darius has to address after x days = 120 + 15(7-x)

so, if the number of invitations should be the same for both of them,

we have to equate their number of invitations

120-15x = 120 + 15(7-x)

subtracting 120 from both the sides,

-15x = 15(7-x) = 105 -15x

adding we 15x on both sides, we wont find any solution for x.

so, this isnt possible or the question must be wrong.

8 0

3 years ago

In 2000, an invasive plant species covered 0.2% of an island. for the 5 years that followed, the area covered by the plant tripl

Elden [556K]

Answer:

The statement is correct

see the explanation

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

$y=a(1+r)^x$

where

y is the area covered by the plant in percentage

x is the time in years since 2000

r is the rate of change

a is the initial value

In this problem we have

$r=200\%=200/100=2$

$a=0.2\%$

substitute the values

$y=0.2(1+2)^x$

$y=0.2(3)^x$

In the year 2005

$x=2005-2000=5\ years$

substitute the value of x in the exponential function

$y=0.2(3)^5=48.6\%$

48.6% is about 50%

therefore

The statement is correct

5 0

4 years ago

How many students studied more than 20 minutes

Crank

9 students.
4 studied 21 minutes,
2 studies 22 minutes,
1 studied 23 minutes,
and 2 studied 30 minutes.
Hope this helps you:)

7 0

3 years ago

Read 2 more answers