How do you find the inverse and range for the following two functions

1) f(x) = (3x - 1) / (2 - 5x)

2) g(x) = |x+4|

I need to find the RANGE (Already got the domains) of both the original function and its inverse. Thank you.

Well, then you are almost done, since if they are one to one functions which are the only functions that can have an inverse function, then all you got to do is to swap the domain and the range of the original for the inverse i.e. the domain of original becomes the range of inverse and the range of original becomes the inverse functions domain.

Edit: so the first one:
Original:
the domain is all the real numbers except x ≠ 2/5
the range is all the real numbers except y ≠ -3/5
Inverse:
the domain is all the real numbers except x ≠ -3/5
the range is all the real numbers except y ≠ 2/5

Now the 2nd one however is not a one to one function, you can quickly determine that by horizontal line test which states if a horizontal line can intercept the graph of a function in more than one point the that function is not one to one, and of course you remember the famous V shaped graph of an absolute value function which a horizontal line would intercept in 2 points. So it is not one to one then it has no inverse.

Regards.

You are welcome, always a pleasure to be of assistance.

Report Abuse