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.
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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? $\displaystyle f(x) = ax+b$ $\displaystyle g(x) = x^2+x+1$ $\displaystyle g(f(x)) = x^2-5x+7$ ??
Last edited by harish21; Apr 23rd 2010 at 11:32 PM.
yes it should be f(x),g(x) and gf(x)
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.
Hi, I did set the equations together in the first place. Now I have had another look and have solved for b. Thanks!
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
Last edited by Neverquit; Apr 24th 2010 at 04:17 AM. Reason: correction
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