Math Help - [SOLVED] find a and b? Simple problem

1. [SOLVED] find a and b? Simple problem

Hi, I have tried this problem a few times.

Fx=ax+b

gx=x^2+x+1

gfx=x^2-5x+7

Not sure where I'm going wrong. A few tips would be appreciated.

2. Originally Posted by Neverquit
Hi, I have tried this problem a few times.

Fx=ax+b

gx=x^2+x+1

gfx=x^2-5x+7

Not sure where I'm going wrong. A few tips would be appreciated.
Your notation is unclear. Did you mean this?

$f(x) = ax+b$

$g(x) = x^2+x+1$

$g(f(x)) = x^2-5x+7$

??

3. correction

yes it should be f(x),g(x) and gf(x)

4. Originally Posted by Neverquit
yes it should be f(x),g(x) and gf(x)
IF
$f(x) = ax+b$

$g(x) = x^2+x+1$

then,

$g(f(x)) = (ax+b)^2+ (ax+b)+1$.......(I)

expand this..

Given $g(f(x)) = x^2-5x+7$.........(II)

equate (I) and (II) to find a and b.

5. update

Hi,
I did set the equations together in the first place. Now I have had another look and have solved for b.
Thanks!

6. Update

From ax^2+ 2abx+b^2+ax+b+1= x^2-5x+7
Set x=0
b^2+b-6=0
(b+3)(b-2)…b=-3,2

For 'A' st b=-3, A=1....or...st b=2, A=-1