# How to solve the function fg(2x)

• Mar 15th 2012, 11:13 AM
BobtheBob
How to solve the function fg(2x)
I've become a bit confused on a question that is:

let $f(x)=x^2-1$ and $g(x)=2x+1$

Calculate $fg(2x)$

I'm not too sure. Is it:

$f(2(2x)+1)$ or $f(2(2x+1))$?

Thanks very much!
• Mar 15th 2012, 11:16 AM
Kanwar245
Re: How to solve the function fg(2x)
I think fg should be 2x^3 + x^2 - 2x - 1 and then you just plug in 2x in place of x to get your ans.
• Mar 15th 2012, 11:23 AM
princeps
Re: How to solve the function fg(2x)
Quote:

Originally Posted by BobtheBob
I've become a bit confused on a question that is:

let $f(x)=x^2-1$ and $g(x)=2x+1$

Calculate $fg(2x)$

I'm not too sure. Is it:

$f(2(2x)+1)$ or $f(2(2x+1))$?

Thanks very much!

$(f \circ g)(x)=(2x+1)^2-1=4x^2+4x$

$(f \circ g) (2x)=4(2x)^2+4\cdot 2x=16x^2+8x$
• Mar 15th 2012, 11:32 AM
BobtheBob
Re: How to solve the function fg(2x)
Ok thanks very much for the help! Much appreciated.
• Mar 15th 2012, 11:37 AM
Kanwar245
Re: How to solve the function fg(2x)
Quote:

Originally Posted by princeps
$(f \circ g)(x)=(2x+1)^2-1=4x^2+4x$

$(f \circ g) (2x)=4(2x)^2+4\cdot 2x=16x^2+8x$

I think that is the wrong way of doing it. it's not fog
• Mar 15th 2012, 12:02 PM
BobtheBob
Re: How to solve the function fg(2x)
Oh right. I originaly got 16x^2 + 8x though although I wasn't sure of it...?