What is the inverse of y=2x + 3? Please show all steps.
First get x on its own:
Subtract 3 from each side
y - 3 = 2x
Divide through by 2
y/2 - 3/2 = x
or x = y/2 - 3/2
Now simply switch labels: x↔y
y = x/2 - 3/2
First switch x and y around to get x=2y+3
Now solve for y
(x-3)/2=y or y=(x-3)/2
If you look carefully gibsonj338 you will see that the two results are the same - they are just expressed slightly differently.
Please correct me if I am wrong Alan but
I think that you have always made a big point of telling me that I am not allowed to swap the x and y over and rearrange afterwards.
I have never understood why but i think it is because you have to be very careful that the inverse is still a function.
That is, in the original function every x value must map to a unique y value (vertical line test)
and if you are going to get an inverse function then every original y value must map to a unique original x value.
So if you take an inverse of a function you may have to limit the domain of the new inverse function or else it may not be a function at all.
Most times I do not think that there is any problem with doing it this way but you have to be careful.
Did I get this it right Alan ?
Yes, but in this case of course it is a simple linear function defined over all the real numbers for both x and y, so it works out ok either way.
I thought it would work anyway so long as I am careful about the restrictions.
It still confuses me. I don't understand why you say I can't do it.
Consider the function y = x2
This doesn't have an inverse (in the real number domain) because there isn't a unique value of x for a given y, but by writing x = y2 before doing anything else you imply there is (to qualify as a function an expression must map an input to a unique output).
However, as you say, the important thing is being careful about the restrictions. As long as you keep this in mind I will not say you can't do it Melody!
Mmm Thanks Alan
I am just thinking here.
$No inverse even with domain restricitions because all x in the domain map to 2 y values$$
My usual way
$But this is not a function so there is no inverse.$$$
Ok I can see that your way is a little tidier :)