# Composite functions

• Feb 10th 2010, 12:24 PM
koumori
Composite functions
Am I working this problem properly?
If $f(x)=3x+1$, and $g(x)=(x^2+5x)^{-\frac{1}{2}}$, find $g(f(x))$.

Working:
If $f(x)=3x+1$, and $g(x)=(x^2+5x)^{-\frac{1}{2}}$ then, $g(f(x))$= $((3x+1)^2+5(3x+1))^{-\frac{1}{2}}$.

Am I correct, and is that the final answer?
• Feb 10th 2010, 12:27 PM
pickslides
Quote:

Originally Posted by koumori
Am I correct,

Yep

Quote:

Originally Posted by koumori
and is that the final answer?

Expand inside the main bracket and group like terms to simplify
• Feb 10th 2010, 03:10 PM
koumori
Quote:

Originally Posted by pickslides
Yep

Expand inside the main bracket and group like terms to simplify

Ok...so the final answer looks like this:
$((9x^2+1)+(15x+5))^{-\frac{1}{2}}\rightarrow \frac{1}{\sqrt{(9x^2+1)+(15x+5)}}$?
• Feb 10th 2010, 03:16 PM
icemanfan
Actually, what you should have found was that the expression simplifies to

$((9x^2 + 6x + 1) + (15x + 5))^{-\frac{1}{2}}$,

and that can be further simplified to

$(9x^2 + 21x + 6)^{-\frac{1}{2}}$.

You can also take out a factor of 3:

$(3(3x^2 + 7x + 2))^{-\frac{1}{2}}$
• Feb 10th 2010, 05:49 PM
pickslides
Quote:

Originally Posted by koumori
Ok...so the final answer looks like this:
$((9x^2+1)+(15x+5))^{-\frac{1}{2}}\rightarrow \frac{1}{\sqrt{(9x^2+1)+(15x+5)}}$?

No, $(3x+1)^2 \neq 9x^2+1$
• Feb 11th 2010, 11:00 AM
koumori
Quote:

Originally Posted by icemanfan
Actually, what you should have found was that the expression simplifies to

$((9x^2 + 6x + 1) + (15x + 5))^{-\frac{1}{2}}$,

and that can be further simplified to

$(9x^2 + 21x + 6)^{-\frac{1}{2}}$.

You can also take out a factor of 3:

$(3(3x^2 + 7x + 2))^{-\frac{1}{2}}$

Quote:

Originally Posted by pickslides
No, $(3x+1)^2 \neq 9x^2+1$

I see! Because I should use F.O.I.L on $(3x+1)^2$ making it
$((9x^2 + 6x + 1) + (15x + 5))^{-\frac{1}{2}}$. Then I have to do simple addition of like terms to net a result of $(9x^2 + 21x + 6)^{-\frac{1}{2}}$. Then do as you said and factor everything by 3.
Finally, expand the exponent so $(9x^2 + 21x + 6)^{-\frac{1}{2}}$ becomes: $\frac{1}{\sqrt{(9x^2 + 21x + 6)}}$

Funny how I lost my head at this once the big words came out......(Surprised).

Thank you for your help guys!