Question

Plot the following two graphs on the same cartesian plain

f(x) = 3x -2
f^ -1(x) = x/3 +2/3

Answer 1

The two functions are 1st degree polynomial, so they are both lines.

In order to draw a line, you have to sample two points and connect them.

To sample points from an equation, choose any value for x and compute the correspondent value for y.

For example, if we choose x=0 and x=1 for the first equation, we have

`f(x)=3x-2 \implies f(0)=-2,\quad f(1)=1`

So, the line passes through the points
`(0,-2)` and
`(1,1)`

Similarly, if we choose x=0 and x=3 for the first equation, we have

`f^(-1)(x)=(x)/(3)+(2)/(3) \implies f(0)=(2)/(3),\quad f(3)=1`

So, this line passes through the points
`\left(0,(2)/(3)\right)` and
`(3,1)`

If you draw the two points for each line and connect the pairs, you'll have the two lines.