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

Step by step, with the reason for every step · Piecewise functions · Algebra 2

Step by step

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

f(x) = x² if x ≤ 2

= x + 1 if x > 2

This is a piecewise function.

It has 2 rules.

Which rule we use depends on x.

Each x uses only one rule.

piecewise: a different rule for different x's

each x uses only one rule

Careful!

2 is an edge: two rules meet there.

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

Careful: x = 2 goes where the "or equal to" is

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

So we use this rule: x².

Put 2 in place of x in x².

f(2) = 2²

2² means 2 times 2.

2² = 2 × 2 = 4

That is 4.

f(2) = 4

So f(2) = 4.

Let's check: does 2 fit each rule's x's?

Only one must say yes.

first rule: 2 ≤ 2 yes

second rule: 2 > 2 no ✗

Only the first rule fits.

So f(2) is right!

Let's look back.

First: find the right piece.

Then: put 2 in.

Last: check.

Answer

f(2) = 4

Try this one yourself, then check:

f(x) = x² if x ≤ 2, x + 2 if x > 2, find f(2)

Show the answer

f(2) = 4