EllipseHard
Question
If f(x) is strictly increasing function then the set of values of ′k′ for which the major axis of the ellipse 
= 1 is the x-axis, is -
= 1 is the x-axis, is -Options
A.k ∈ R
B.k ∈ R - {1}
C.k ∈ [1, 3] ∪ (5, ∞)
D.k > 1
Solution
∴ Major Axis is x-axis
⇒ f(eln(k-1)+k) >
⇒ eln(k-1)+k >
(∵ f is increasing)
⇒ (k - 1).ek > (k - 1).k
(∵ k - 1 > 0 from domain)
⇒ ek > k which is true for all k ∈ R but k - 1 > 0 i.e. k > 1.
⇒ f(eln(k-1)+k) >
⇒ eln(k-1)+k >
(∵ f is increasing)⇒ (k - 1).ek > (k - 1).k
(∵ k - 1 > 0 from domain)
⇒ ek > k which is true for all k ∈ R but k - 1 > 0 i.e. k > 1.
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