If f(x) = x^2 - 2 and g(x) = 3x + 1, what is f(g(1))? Step by Step

Step by step

The question

Question: find f(g(1)) for f(x) = x² − 2 and g(x) = 3x + 1.

f(x) = x² − 2

There are four choices.

First we solve it, the normal way.

Then we pick.

g(x) = 3x + 1

1 Work out the inside

f(g(1)) is a function inside a function.

Like with brackets, we start inside.

f works on what g(1) gives.

So first g(1).

inside first: g(1)

1 → g → f

Put 1 in place of x in g.

We write it in brackets: 3x becomes 3 times 1, not 31.

g(1) = 3(1) + 1

Everyone uses the same order, so we all get the same answer.

Times comes before plus.

3(1) means 3 times 1.

Order: × ÷ → + −

3(1) = 3 × 1

3 times 1 is 3.

= 3 + 1

3 plus 1 is 4.

g(1) = 4

2 Then the outside

g(1) is 4.

So f(g(1)) is f(4).

f(g(1)) = f(4)

Put 4 in place of x in f.

= 4² − 2

Everyone uses the same order, so we all get the same answer.

Powers come before minus.

Order: Powers → + −

4² means 4 times 4.

4² = 4 × 4

= 16

That is 16.

= 16 − 2

16 minus 2 is 14.

f(g(1)) = 14

So f(g(1)) = 14.

3 Pick the choice

Our answer is f(g(1)) = 14.

That is choice C.

C) 14

4 Why not the others

A is −4.

Wrong: multiplied f(1) by g(1).

A) −4 ✗ multiplied f(1) by g(1)

B is −2.

Wrong: that is g(f(1)): in f(g(1)), g goes first.

B) −2 ✗ that is g(f(1)): in f(g(1)), g goes first

D is 16.

Wrong: forgot the − 2: f(4) = 16 − 2.

D) 16 ✗ forgot the − 2: f(4) = 16 − 2

Let's look back.

First: work out the inside.

Then: then the outside.

Then: pick the choice.

Last: why not the others.

Answer