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MATH / Let f(x)=√(ax²+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?

Problem

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problem

Let f(x)=ax2+bxf(x) = \sqrt{ax^2 + bx}. For how many real values of aa is there at least one positive value of bb for which the domain of ff and the range of ff are the same set?
Plain-text mathematical notation (without MathML)
Let f(x)=√(ax²+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?
Original LaTeX notation
Let $f(x) = \sqrt{ax^2 + bx}$. 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?

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
3afbdcb9-2506-53f4-a1c5-49a47e3c4fd8
task_key
intermediate~5falgebra--test--3afbdcb9-2506-53f4-a1c5-49a47e3c4fd8
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import