JEE Main 2019MathematicsFunctionsComposite FunctionsmediumMCQ
JEE Main 2019 — Functions Question with Solution
From: JEE Main 2019 (Online) 10th April Morning Slot
Question
Let f(x) = ex – x and g(x) = x2 – x, ∀ x ∈ R. Then the set of all x ∈ R, where the function h(x) = (fog) (x) is increasing, is :
Choose an option
▸Show full solutionCorrect option: D
Correct answer
D[0,21]∪[1,∞)
Step-by-step explanation
f(x) = ex – x, g(x) = x2 – x
f(g(x)) = e(x2 - x) - (x2 - x)
If f(g(x)) is increasing function
(f (g(x)))x = e(x2−x)×(2x−1)−2x+1
⇒A(2x−1)B[e(x2−x)−1]
A & B are either both positive or negative
for (f (g(x)))'≥ 0,
x∈[0,21]∪[1,∞)
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Functions chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
This is a previous-year question from JEE Main 2019, 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.
