graph f and its inverse

Question

So f would be a graph, and f^-1 would be its inverse, im asked to graph on the same axis. How would i graph a value and its inverse on the same axis? 

 

Answer 1

Suppose you have this function:

f(x) =  5 x

Graphically this would represent: y = 5x. 

Now let us find the inverse of this. x = 1/5 y. Or g(y) = 1/5 y. Since "y" is simply a symbol, you can write the inverse function now back with x:

g(x) = 1/5 x

or

f^-1(x) = 1/5 x.

Now you can plot them together.

Answer 2

f  and f^-1 are y and y^-1.

 

If you graph them simultaneously as y₁ and y₂ on the graphing calculator, you will have graphed them on the same axis.

Check the setup on your calculator to see the increments on the axes.