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

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==Problem==
 
==Problem==
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?
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Let <math>\displaystyle f(x)= \sqrt{ax^2+bx} </math>.  For how many [[real number | real]] values of <math>a</math> is there at least one [[positive number | positive]] value of <math> b </math> for which the [[domain]] of <math>f </math> and the [[range]] of <math> f </math> are the same [[set]]?
  
 
<math> \mathrm{(A) \ 0 } \qquad \mathrm{(B) \ 1 } \qquad \mathrm{(C) \ 2 } \qquad \mathrm{(D) \ 3 } \qquad \mathrm{(E) \ \mathrm{infinitely \ many} }  </math>
 
<math> \mathrm{(A) \ 0 } \qquad \mathrm{(B) \ 1 } \qquad \mathrm{(C) \ 2 } \qquad \mathrm{(D) \ 3 } \qquad \mathrm{(E) \ \mathrm{infinitely \ many} }  </math>
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==See Also==
 
==See Also==
 
*[[2003 AMC 12A Problems/Problem 24 | Previous problem]]
 
*[[2003 AMC 12A Problems/Problem 24 | Previous problem]]
*[[2003 AMC 12A]]
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*[[2003 AMC 12A Problems]]
  
 
[[Category:Intermediate Algebra Problems]]
 
[[Category:Intermediate Algebra Problems]]

Revision as of 16:33, 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 of $f$ are the same set?

$\mathrm{(A) \ 0 } \qquad \mathrm{(B) \ 1 } \qquad \mathrm{(C) \ 2 } \qquad \mathrm{(D) \ 3 } \qquad \mathrm{(E) \ \mathrm{infinitely \ many} }$

Solution

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See Also

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