JEE Main20241 Feb 2024Morning ShiftMathematicsFunctionsActual
Let f : R → R and g : R → R be defined as f x = log e x , x > 0 e − x , x ≤ 0 and g x = x , x ≥ 0 e x , x < 0 . Then, g o f : R → R is:
Options
- Aone-one but not onto
- Bneither one-one nor onto
- Conto but not one-one
- Dboth one-one and onto
Correct answer
B. neither one-one nor onto
Step-by-step solution
Given: f x = log e x , x > 0 e − x , x ≤ 0 and g x = x , x ≥ 0 e x , x < 0 ⇒ g f x = f x , f x ≥ 0 e f x , f x < 0 ⇒ g f x = e − x , − ∞ , 0 e log x , 0 , 1 log x , 1 , ∞ Graph of g f x is given below: Range of g f x = [ 0 , ∞ ) ≠ Codomain So, g f x is many-one and into.