Step by step
The question
Question: find f(a − 1) for f(x) = 2x + 3.
f(x) is read "f of x".
It is a rule, called a function.
A number goes in for x.
The rule gives one answer out.
1 Put the bracket in
f(a − 1) means: put a − 1 in place of every x.
We write (a − 1) in brackets.
It goes in as one piece.
2 Open the brackets
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
Watch the signs.
2 times a is 2a.
2 times (−1) is −2.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
Each colour is one kind.
−2 + 3 is 1.
So the expression is 2a + 1.
4 Check
Let's check.
We pick a number for each letter: a = 2.
We put it into the start.
Now into our answer.
Both give 5.
Same value, so 2a + 1 is right!
Let's look back.
First: put the bracket in.
Then: open the brackets.
Then: group like terms.
Last: check.