Difference between revisions of "2003 AMC 12A Problems/Problem 25"

 
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Let <math> f(x) = sqrt{ ax^2 + bx } </math>. For how many real values of <math>a</math> is there at least one positive value of <math> b </math> for which the domain of <math>f </math> and the range <math> f </math> are the same set?
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Let <math> f(x)=</math> <math> \sqrt{ax^2+bx} </math>
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For how many real values of <math>a</math> is there at least one positive value of <math> b </math> for which the domain of <math>f </math> and the range <math> f </math> are the same set?
  
 
(A)0  (B) 1  (C) 2  (D) 3  (E) infinitely many
 
(A)0  (B) 1  (C) 2  (D) 3  (E) infinitely many

Revision as of 10:49, 28 November 2006

Let $f(x)=$ $\sqrt{ax^2+bx}$ For how many real values of $a$ is there at least one positive value of $b$ for which the domain of $f$ and the range $f$ are the same set?

(A)0 (B) 1 (C) 2 (D) 3 (E) infinitely many

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