# Thread: f o g = h.

1. ## f o g = h.

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.

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

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

4. Originally Posted by Plato
Does $g(x)=x^2+x-1$ work? Why or why not?
Can you please clarify this for me !

5. 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!

6. 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.

7. 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)

8. 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 .