NTA Abhyas JEE Main2020MathematicsContinuity and DifferentiabilityPractice

Let f x = x and g x = x , (where, . denotes the greatest integer function). Then, f o g ′ − 1 is

Options

A0
Bdoes not exist
C- 1
D1

Correct answer

B. does not exist

Step-by-step solution

f o g x = f g x = f x = x Now, LHL of f o g ′ − 1 = lim h → 0 + f o g − 1 − h − f o g − 1 − h = lim h → 0 + ⁡ - 1 - h - - 1 - h = lim h → 0 + ⁡ - 2 - - 1 - h = lim h → 0 + ⁡ 1 - h → - ∞ ∴ f o g ′ − 1 does not exist.

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