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Need help with inverse functions!

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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! XD

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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! XD

 

 

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 

    → g(x) = x / (x - 2)

     

  2. Change g(x) to y

    → y = x / (x - 2)

     

  3. Change y to x, and x to y 

    → x = y / (y - 2)

     

  4. Solve for y 

    → x = y / (y - 2)

    → x (y - 2) = y

    → xy - 2x = y

    → xy - y = 2x

    → y (x - 1) = 2x

    → y = 2x / (x - 1)

     

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

    → y = 2x / ( x - 1)

    → g-1 (x) = 2x / (x - 1)

 

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

Hope this was helpful!

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