# Need help with inverse functions!

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Hi Guys !

I need help on this!!!

find g-1 (5)

g= x/x-2, not equal to 2

Thanks!

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When dealing with inverses, I always switch the x and y in the original function and isolate y to get the inverse function.

For rational functions, it's a bit trickier:

y = g(x)

y = x/(x-2), x is not 2

Switch x and y

x = y/(y-2)

Now the next parts are easier than you think. Just multiply both sides by y, expand:

xy - 2x = y

Then isolate the 'y's, factor y out, and isolate y.

y = 2x/(x-1)

Then you know that g-1 = 2x/(x-1). Just substitute 5 in there.

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When dealing with inverses, I always switch the x and y in the original function and isolate y to get the inverse function.

For rational functions, it's a bit trickier:

y = g(x)

y = x/(x-2), x is not 2

Switch x and y

x = y/(y-2)

Now the next parts are easier than you think. Just multiply both sides by y, expand:

xy - 2x = y

Then isolate the 'y's, factor y out, and isolate y.

y = 2x/(x-1)

Then you know that g-1 = 2x/(x-1). Just substitute 5 in there.

Here's where I don't understand how you got there.. Can you explain all the steps, please!

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Here wait, we have just studied this so I should be able to help you. The guy who replied is right, what do you not understand?

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When dealing with inverses, I always switch the x and y in the original function and isolate y to get the inverse function.

For rational functions, it's a bit trickier:

y = g(x)

y = x/(x-2), x is not 2

Switch x and y

x = y/(y-2)

Now the next parts are easier than you think. Just multiply both sides by y, expand:

xy - 2x = y

Then isolate the 'y's, factor y out, and isolate y.

y = 2x/(x-1)

Then you know that g-1 = 2x/(x-1). Just substitute 5 in there.

Here's where I don't understand how you got there.. Can you explain all the steps, please!

I'll try to explain, as I used to not understand that part as well

So, to find the inverse function of g(x) (, and basically, any other functions):

1. Write down the equation

â†’ g(x) = x / (x - 2)

2. Change g(x) to y

â†’ y = x / (x - 2)

3. Change y to x, and x to y

â†’ x = y / (y - 2)

4. Solve for y

â†’ x = y / (y - 2)

â†’ x (y - 2) = y

â†’ xy - 2x = y

â†’ xy - y = 2x

â†’ y (x - 1) = 2x

â†’ y = 2x / (x - 1)

5. Your new equation is the inverse of g(x)

â†’ y = 2x / ( x - 1)

â†’ g-1 (x) = 2x / (x - 1)

And to solve g-1(5), â€‹as by.andrew said, you just put 5 instead of x in the function

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Thanks !!:-)

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