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4 years ago

What is the inverse function of f(x)= x/x-2?

Mathematics

1 answer:

jarptica [38.1K]4 years ago

5 0

Answer:

$f^{-1}(x)=\frac{2x}{x-1}$

Step-by-step explanation:

Start by replacing f(x) by the variable "y" and solving for x in the equation:

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

Now do the final replacement using the inverse function notation, and replacing "y" with "x":

$x=\frac{2y}{y-1} \\f^{-1}(x)=\frac{2x}{x-1}$

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4 years ago

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A man starts at a point A and walks 18 feet north. He then turns and walks due east at 18 feet per second. If a searchlight plac

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Answer:

1/10 per sec

Step-by-step explanation:

When he's walked x feet in the eastward direction, the angle Θ that the search light makes has tangent

tanΘ = x/18

Taking the derivative with respect to time

sec²Θ dΘ/dt = 1/18 dx/dt.

He's walking at a rate of 18 ft/sec, so dx/dt = 18.

After 3seconds,

Speed = distance/time

18ft/sec =distance/3secs

x = 18 ft/sec (3 sec)

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3 years ago

Eva earns $16 for walking dogs for 4 hours. If eva charges at the same rate, how many hours will it take her to earn $32

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Step-by-step explanation:

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3 years ago

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In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through 1 12 of a circle. Through how

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Answer:

3/2π and π/480

Step-by-step explanation:

The question given says that the minute hand on a clock moves through complete circle in 1 hour, that is 360° or 2π. It also says that the hour hand moves through 1/12 of a circle, that means 30° or π/6.

To know how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m, it's necessary to calculate how many radians move them per minute.

Between 1:00 p.m. and 1:45 p.m 45 minutes have passed. With that information, the radians can be calculated using multiplication and division.

Minute hand: To know how many radians move the minute hand per minute division wil be used.

Movement in an hour/ minutes in an hour

2π rad/60 min= π/30 rad-min

That means the minute hand move π/30 radians in a minute.

Now, multiplication can be used to calculate how many radians move the minute hand in 1h.

(π/30 rad-min)(45 minutes)= 3/2π rad

The minute hand moves 3/2π radians between 1:00 p.m. and 1:45 p.m.

Hour hand: To know how many radians move the hour hand per minute division wil be used.

Movement in an hour/ minutes in an hour

2π rad/(60 min x 12 hours)= π/360 rad-min

That means the minute hand move π/360 radians in a minute.

Now, multiplication can be used to calculate how many radians move the hour hand in 1h.

(π/360 rad-min)(45 minutes)= π/8 rad

The minute hand moves π/8 radians between 1:00 p.m. and 1:45 p.m.

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3 years ago

What is the inverse function of f(x)= x/x-2?​

What is the inverse function of f(x)= x/x-2?