Solve f(x) = 3x, g(x) = x + 2, g(f(x))

Step by step

The question

Question: find g(f(x)) for g(x) = x + 2 and f(x) = 3x.

1 Work out the inside

g(f(x)) is a function inside a function.

Like with brackets, we start inside.

First f(x).

f(x) is 3x.

So g(f(x)) is g(3x).

2 Put it in

Put (3x) in place of every x in g.

We keep it in brackets.

3 Open the brackets

A bracket with a plus or nothing in front can just be removed.

Now we have 3x + 2.

4 Check

Let's check.

We pick a number for each letter: x = 2.

We put it into the start.

Now into our answer.

Both give 8.

Same value, so 3x + 2 is right!

Let's look back.

First: work out the inside.

Then: put it in.

Then: open the brackets.

Last: check.