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3 years ago

I need help with this?

Mathematics

1 answer:

kogti [31]3 years ago

8 0

Answer:

y = 3( $0.5^{x}$ )

Step-by-step explanation:

Exponential function has the form f(x) = k $b^{x}$ where b > 0 and b ≠ 1

~~~~~~

3 = k × $b^{0}$ ⇒ k = 3

1.5 = 3( $b^{1}$ ) ⇒ b = 0.5

Thus, y = 3(  $0.5^{x}$  )

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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.

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3 years ago

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Answer:

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3 years ago

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Which linear function has the greater rate of change Y= 8x+ 3

Ad libitum [116K]

17 bc I did it trust me pls

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3 years ago

A crew has paved 3/4 of a mile of road. If they have completed 50% of the work, how long is the road they are paving?

mel-nik [20]

Answer:

1.5

Step-by-step explanation:

Let the value be x,

(3/4) = 50% * x

x = 1.5

Thenks and mark me brainliest :))

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3 years ago

Twelve more then the product of 5 and a number x? x is 2

yaroslaw [1]

Answer:

Step-by-step explanation:

5 * 2 = 10

10 + 12 (because 12 more)

=22

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3 years ago