Thread: Inverse functions and symmetry

I have the line y=ax + b
I am told that y=-ax + b is an inverse of the first line. Why is this so? I know that inverses are symmetrical about the line y=x. I graphed y=ax+3 and y=-ax+3, and they do not seem symmetrical about the line y=x to me.

Because the statement is not true, you can determine the inverse of by changing and and solve back to y=.., like this:

Calculating the inverse:


For example:

The inverse function has to be


Now look at the graphs of this functions, they're symmetrical towards the first bissectrice (y=x).

To find the inverse function of y= ax+b, replace x for y and y for x, then solve for y:
x=ay+b inverse: y= (x-b)/a
for instance: y = 3x +2 The inverse: y = (x-2)/3. Try the graph, they are symmetrical to the line y=x.

Hey Siron we must have similar minds!

Originally Posted by BERMES39

Hey Siron we must have similar minds!

Yes, I was thinking the same!

So the two equations I are NOT inverses?

is indeed not the inverse function of

Like you said, if you graph these lines then they're not symmetrical to the first bissectrice ( ).

Have you graphed the example I and BERMES39 have given you?