MathDB
Same Domain + Range

Source:

February 20, 2008
algebrafunctiondomainconicsparabolacalculusinequalities

Problem Statement

Let f(x)\equal{}\sqrt{ax^2\plus{}bx}. For how many real values of a a is there at least one positive value of b b for which the domain of f f and the range of f f are the same set? <spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> infinitely many <span class='latex-bold'>(A)</span>\ 0 \qquad <span class='latex-bold'>(B)</span>\ 1 \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ 3 \qquad <span class='latex-bold'>(E)</span>\ \text{infinitely many}