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# inverse functions, domain and range watch

1. f(x)=1/x ( X≤3) X is real

can someone show me how to do the inverse function domain and range,

thankyou
2. These are the steps i follow to find the inverse function.
Change the f(x) to Y....
Y = 1/x

Swap the X and the Y's around (this makes no sense mathamatically, but it works!)
X = 1/Y

Now make Y the subject
Y = 1/X
F^-1(x) = 1/x

lool, thats exactly the same! Therefore, there must be some other way of working it out...

The inverse function's Domain is always the functions range, and the inverse functions range is always the
The DOMAIN is a comment about the X values. for F(x), thats X<3 (as said in the question)
Therfore the RANGE of the INVERSE is Y<3

To find the range for f(x), draw out the graph of y = 1/x. Find a comment about the Y values for this graph. I think, whilst picturing it in my head, the range for f(x) is 0 > y > 0 (so basically Y can be any value except for 0)

Now, this means that for the domain of the inverse is 0 > X > 0

D of f(x) = R of INVf(x)
R of f(x) = D of INVf(x)

^learn that, it's a good way of getting marks.

Hope this is correct and helps!

Edit: when drawing f(x), remember about the restriction [x<3]. The domain i've said for INVf(x) is incorrect because i forgot to take this into account. Hopefully you can come up with the domain urself.
3. (Original post by AmyTownshend)
f(x)=1/x ( X≤3) X is real

can someone show me how to do the inverse function domain and range,

thankyou

now swap the x and the y around and rearrange to make y the subject.

You should get

Now the domain for the inverse function is the range of the original function and the inverse of this is the range of the original function

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