Please help me I really need someone's help!?

Question

I asked this question before but no one answered :(

I am in pre calc and I need to solve this:

Well, this is my question: I need to find the range of f^-1(x) AKA inverse of y = (x+1)/(x+2). So, here is my thought process:

x = (y+1)/(y+2)
xy + 2x = y + 1
xy - y = - 2x + 1
y(x - 1) = - 2x + 1
y = (-2x + 1) / ( x - 1)
Hence:
F inverse of x = (-2x + 1) / (x - 1)

The range should be all real numbers, right? I got marked wrong on my quiz. Can someone please help me? Even when I graphed it, it seemed as if it was all real "y".....what am I doing wrong?

BTW, I havent learned yet how to do derivatives.....but still help!!!

Answer 1

is not all real number because x can't be 1

if x was 1 then the denominator would be 0 and you can NEVER have 0 on the denominator. aka u can't divide by zero

so u should have said for the range, x (not equal to sign) 0

or u can say x = all R except for 1

Answer 2

God I haven't done inverses in so long.
However I can see that x cannot equal 1. Since x cannot equal 1 then there is certainly a hole there in the possible y values.

Hope this helped. Didn't the teacher go over this?