A function f from a set X to Y is called onto, if for every y ∈ Y there exist x ∈ X such…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
A function f from a set X to Y is called onto, if for every
y ∈ Y there exist x ∈ X such that f (x) = y. Unless the contrary is specified, a real function is onto if it takes all real values, otherwise it is called into function. Thus, if X and Y are finite sets, then f cannot be onto If Y contains more element than X.
The function f (x) = \(\frac{x^{2}+2 x+c}{x^{2}+4 x+3 c}\) is onto, if
- 0 < c < 2
- 0 < c < 4
- \(-\frac{1}{2}<\mathrm{c}<\frac{1}{2}\)
- 0 < c < 1
Answer
(D) 0 < c < 1
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