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 16:29, 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
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