# [SOLVED] find a and b? Simple problem

• Apr 23rd 2010, 10:58 PM
Neverquit
[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.
• Apr 23rd 2010, 11:14 PM
harish21
Quote:

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?

\$\displaystyle f(x) = ax+b\$

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

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

??
• Apr 23rd 2010, 11:18 PM
Neverquit
correction
yes it should be f(x),g(x) and gf(x)
• Apr 23rd 2010, 11:35 PM
harish21
Quote:

Originally Posted by Neverquit
yes it should be f(x),g(x) and gf(x)

IF
\$\displaystyle f(x) = ax+b\$

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

then,

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

expand this..

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

equate (I) and (II) to find a and b.
• Apr 24th 2010, 02:39 AM
Neverquit
update
Hi,
I did set the equations together in the first place. Now I have had another look and have solved for b.
Thanks!
• Apr 24th 2010, 03:13 AM
Neverquit
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