Lesson: Function Notation

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

Hi Brent,

Could you please help me to solve the following questions taken from a practice test?

For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b ?

f(x) = x^2
f(x) = x + 1
f(x)= sqrt{x}
f(x)= 2/x
f(x) = –3x

Thank you!
gmat-admin's picture

I'm happy to help.
Here's my full solution: https://gmatclub.com/forum/for-which-of-the-following-functions-is-f-a-b...


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