Question

Graph the original line and its inverse.
1. f(x)=5x+1
2. f(x)= x+8/4
3. g(x)=2x-3/4
4. h(x)=1/2(x+2)-3

i need help thank you.

Answer 1

So the general definition of an inverse is this. If your function F generates the points
\[(X _{1},Y _{1}) , (X _{2},Y _{2}), etc.\]
Then your inverse function will be the points
\[(Y _{1},X _{1}) , (Y_{2},X _{2}), etc.\]
One graphical trick to finding this is to graph your function, and then graph the line Y=X. Next, you're going to (this is a bit hard to explain) reflect your function around the line Y=X. Let me see if I can draw an example.



The curve on the right is f(x), the curve on the upper left is its inverse. If you start with something simple like a linear function, and try plotting a few points and their inverses (that is, (X,Y) for f, and (Y,X) for the inverse,) you'll see what I mean by "reflecting" around the line Y=X.