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

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==Problem==
 
==Problem==
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>\displaystyle 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?
  
 
(A)0  (B) 1  (C) 2  (D) 3  (E) infinitely many
 
(A)0  (B) 1  (C) 2  (D) 3  (E) infinitely many
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==See Also==
 
==See Also==
[[2003 AMC 12A Problems/Problem 24 | Previous problem]]
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*[[2003 AMC 12A Problems/Problem 24 | Previous problem]]
[[2003 AMC 12A]]
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*[[2003 AMC 12A]]
  
 
[[Category:Intermediate Algebra Problems]]
 
[[Category:Intermediate Algebra Problems]]

Revision as of 16:27, 28 November 2006

Problem

Let $\displaystyle f(x)= \sqrt{ax^2+bx}$. 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

== Solution==

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