JEE Main202311 Apr 2023Evening ShiftMathematicsContinuity and DifferentiabilityActual
Let f and g be two functions defined by f x = x + 1 , x < 0 x - 1 , x ≥ 0 and g x = x + 1 , x < 0 1 , x ≥ 0 .Then g o f x is
Options
- AContinuous everywhere but not differentiable exactly at one point
- BContinuous everywhere but not differentiable at x = 1
- CDifferentiable everywhere
- DNot continuous at x = 1
Correct answer
A. Continuous everywhere but not differentiable exactly at one point
Step-by-step solution
Given, f x = x + 1 ,             x < 0 x - 1 ,     x ≥ 0 and g x = x + 1 ,             x < 0 1 ,                         x ≥ 0 ⇒ f x = x + 1 , x < 0 1 - x , 0 ≤ x < 1 x - 1 , x > 1 &   g x = 1 + x , x < 0 1 , x ≥ 0 Now, for g o f x   g o f x = 1 + f x , f x < 0 ,   x < 0 1 , f x ≥ 0 ,   x ≥