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

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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? | 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 | + | <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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+ | == Solution== | ||

{{solution}} | {{solution}} | ||

## Revision as of 17:29, 28 November 2006

## Problem

Let . For how many real values of is there at least one positive value of for which the domain of and the range are the same set?

## Solution

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*