# Solving the inverse of a function

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Yo guys! I did this in my tenth and due to a years gap I can't recollect the correct technique, care to guide me?

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I've heard that this in Maths St is more difficult than in Maths HL this is how I usually do it though:

1. look for points where the graph cuts the x-axis. this will become a vertical asymptote (|).

2. if there is a vertical asymptote, it will become a zero.

3. if there is a horizontal asymptote (---), it will stay as an asymptote but in a different position (1/y)

4. split the graph to sections based on the shapes. also split if it's passed through the x-axis. look at them one by one, section by section.

5. for any point where y=1 or -1, that point will stay there.

6. just imagine the inverse and try to connect them.

I suck at explaining :/ I could've explained better if there was a question example

but say if y=0.5, it would become 2. if y=10 then it would be very close to the x-axis. imagine it...

if you don't get it ask again. or I hope someone could explain this better.

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Yo guys! I did this in my tenth and due to a years gap I can't recollect the correct technique, care to guide me?

Well what I do is switch the x and the y values and then solve for y.

For example

Find the inverse of f(x)=2x-3

1) Replace f(x) with y

y = 2x-3

2) Switch the x's and y's

x= 2y-3

x+3=2y

(x+3)/2 =y

Therefore f-1(x) =(x+3)/2

However don't forget that the inverse of a function isn't always a function because a function has only one value of y for every value of x. (For example, the inverses of quadratic functions are not functions). So if you are asked to find the inverse function,

you have to set restrictions on your inverse to make it a function.

To visualize inverses:

Remember to graph the inverse of a function you reflect it across the line y=x. The x and y values of the inverse will be switched. If (1,0) is a point on f(x), (0,1) is a point on f-1(x).

Sorry if that didn't make sense.... :/

Edited by SmilingAtLife:)

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Actually the method I know is the same as SmilingAtLife's I just first solve in terms of x and then switch y for x. Usually finding the inverse of a function is pretty easy and you may find only 4-5 tricky examples but the above method always works

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oh my God...

I thought you were talking about the inverse graph reciprocal function -________-

sorry! hehe -____-

*geez what's wrong with me today -____-

Edited by Desy Glau

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Thanks guys that was really fast and helpful too!

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I've heard that this in Maths St is more difficult than in Maths HL this is how I usually do it though:

1. look for points where the graph cuts the x-axis. this will become a vertical asymptote (|).

2. if there is a vertical asymptote, it will become a zero.

3. if there is a horizontal asymptote (---), it will stay as an asymptote but in a different position (1/y)

4. split the graph to sections based on the shapes. also split if it's passed through the x-axis. look at them one by one, section by section.

5. for any point where y=1 or -1, that point will stay there.

6. just imagine the inverse and try to connect them.

I suck at explaining :/ I could've explained better if there was a question example

but say if y=0.5, it would become 2. if y=10 then it would be very close to the x-axis. imagine it...

if you don't get it ask again. or I hope someone could explain this better.

The effort counts!

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