JEE Main 2020MathematicsFunctionsMediumMCQ

JEE Main 2020 — Functions Question with Solution

JEE Main 2020 (08 Jan Shift 2)

Question

Let f:1, 3→R, be a function defined by fx=xx1+x2, where x, denotes the greatest integer ≤x. Then the range of f, is

Choose an option

Show full solutionCorrect option: B
Correct answer
B25, 12∪35, 45

Step-by-step explanation

f :1,3→R, fx=xx1+x2

fx=x1+x2,x∈1, 22x1+x2,x∈[2, 3)

f'x=1+x21-x2x1+x22,x∈1, 21+x22-2x2x1+x22,x∈[2,3)

f'x=1-x21+x2,x∈1, 21-2x21+x2,x∈[2,3)

∴ fx is decreasing function.
∴ Rf ∈25, 12∪610, 45

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About this question

This is a previous-year question from JEE Main 2020, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.