Lesson: Function Notation

Rate this video: 

Comment on Function Notation

Hi Brent,

I'm a touch confused with something. I was doing one of the early reinforcement questions and it asked:
If f(x) = 3x − √x and g(x) = x^2, what is f(g(4))?

How exactly do you read out "f(g(4))"? I was confused as to what exactly the question was asking? It seems to me that is asking 'what is f(x) if g(4)?". Is that correct? The problem is that I couldn't see that until I saw your solution in the GMAT Club forums.

Here's the link to the question: https://gmatclub.com/forum/if-f-x-3x-x-and-g-x-x-2-what-is-f-g-209750.html

Thanks for any help,
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-f-x-3x-x-and-g-x-x-2-what-is-f-g-209750.html

The notation f(g(4)) represents the value of the function (f) when we input the value of g(4)

So, in this example, g(4) = 4² = 16

So, f(g(4)) = f(16) [now we must evaluate f(16)]

f(16) = 3(16) − √16
= 48 - 4
= 44

So, to recap, f(g(4)) = f(16) = 44

Does that help?


Awesome! That confirms my assumption. Thanks! :D

Add a comment

Ask on Beat The GMAT

If you have any questions, ask them on the Beat The GMAT discussion forums. The average response time is typically less than 30 minutes.

Change Playback Speed

You have the option of watching our videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and we’ll answer it as fast as humanly possible.

Free “Question of the Day” emails!