Need help with inverse functions!

[Noticeably Absent]

Hi Guys ! 

 

 

I need help on this!!!

 

 

find g^-1 (5)

 

 

 

 

 

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

 

 

Thanks!

[by.andrew]

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. 

[Noticeably Absent]

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!

[elihid98]

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? 

[spacescampi]

 

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 

   → 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!

[Noticeably Absent]

Thanks !!:-)