Graph f(x) = x/3 + 1 and its inverse Step by Step

Step by step

The question

Question: graph f(x) = x/3 + 1 and its inverse.

f(x) = x3 + 1

The inverse goes back: what comes out of f goes in, and what went in comes out.

inverse: swaps in and out

Careful!

The little −1 is a name, not a power.

The inverse is not 1 over f.

Careful: f ⁻¹(x) is not 1f(x)

1 Make a table for f

We pick −3, 0 and 3 for x and work out f.

For example, f of 0 is 1.

2 Swap x and y

For the inverse, every pair swaps: (0, 1) becomes (1, 0).

What came out now goes in.

3 Draw f

Draw the grid.

Plot the points of f.

Join them: the line of f(x) = x/3 + 1.

4 Draw the inverse

Now the swapped points.

Join them: the line of the inverse, f⁻¹.

5 The mirror line

Draw the line y = x.

The two lines are mirror images in it.

Fold the page along y = x, and f lands on f⁻¹.

6 Check

Let's check.

(−3, 0) and (0, −3) are twins.

The line between them crosses y = x at its middle: the same distance on both sides.

The inverse lesson gives the rule f⁻¹(x) = 3(x − 1).

Put in 0: we get −3.

So (0, −3) is on the red line.

It works!

f ⁻¹(0) = 3(0 − 1) = 3(−1) = −3

Let's look back.

First: make a table for f.

Then: swap x and y.

Then: draw f.

Then: draw the inverse.

Then: the mirror line.

Last: check.

Answer