f o g = h.

**ryan18** · January 21st 2010, 08:56 AM

If f(x) = 2x + 8 and h(x) = 2x2 + 2x + 6, find a function g such that f

g = h.

I thought I had a handle on these questions until I got to this one. I have an answer but I am 95% sure it isnt right.

$((x^2)/2)-14x-26$

Like I said I am pretty sure its not right.

**Plato** · January 21st 2010, 09:09 AM

Does $g(x)=x^2+x-1$ work? Why or why not?

**ryan18** · January 21st 2010, 09:11 AM

Wow I am an idiot. I tend to overcomplicate things greatly. Thanks haha.

**Aladdin** · January 21st 2010, 09:43 AM

Originally Posted by Plato

Does $g(x)=x^2+x-1$ work? Why or why not?

Can you please clarify this for me !

**ryan18** · January 21st 2010, 09:48 AM

Its a function f(g(x))=h correct? So you take the function of g, which in this case we found to be x^2+x-1 and plug that into the x values of f(x).

Doing so will give you 2(x^2+x-1)+8.
Factoring out will give you 2x^2+2x-2+8, add like terms and you will come to h, which is 2x^2+2x+6!

**Plato** · January 21st 2010, 09:50 AM

Originally Posted by Aladdin

Can you please clarify this for me !

Well is it true that $f \circ g(x) = h(x)?$
Now you must understand function composition to do that.

**Aladdin** · January 21st 2010, 09:53 AM

Originally Posted by ryan18

So you take the function of g, which in this case we found to be x^2+x-1

You guessed !! g(x)

**Aladdin** · January 21st 2010, 09:56 AM

Originally Posted by Plato

Well is it true that $f \circ g(x) = h(x)?$
Now you must understand function composition to do that.

Yes , for sure .

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