f(x) = 5 - 2x if x <= -1, x^2 if x > -1, find f(-1)

Step by step

The question

Question: find f(−1) for f(x) = 5 − 2x if x ≤ −1, x² if x > −1.

This is a piecewise function.

It has 2 rules.

Which rule we use depends on x.

Each x uses only one rule.

Careful!

−1 is an edge: two rules meet there.

It belongs to the rule with the "or equal to" sign.

1 Find the right piece

Let's see where each rule works on a number line.

So we use this rule: 5 − 2x.

2 Put −1 in

Put −1 in place of x in 5 − 2x.

We write it in brackets.

Times comes before minus.

2(−1) means 2 times −1.

Plus times minus is minus.

2 times 1 is 2.

So we get −2.

Taking away a negative is the same as adding.

So 5 − (−2) becomes 5 + 2.

5 plus 2 is 7.

So f(−1) = 7.

3 Check

Let's check: does −1 fit each rule's x's?

Only one must say yes.

Only the first rule fits.

So f(−1) is right!

Let's look back.

First: find the right piece.

Then: put −1 in.

Last: check.