JEE Advanced2008MathematicsApplication of DerivativesActual
Let the function g:(- , ) (- 2 , 2 ) be given by g(u)=2 ⁻¹ (e^u )- 2 . Then, g is
Options
- Aeven and is strictly increasing in (0, )
- Bodd and is strictly decreasing in (- , )
- Codd and is strictly increasing in (- , )
- DNeither even nor odd, but is strictly increasing in (- , )
Correct answer
C. odd and is strictly increasing in (- , )
Step-by-step solution
g(u)=2 ⁻¹ (e^u )- 2 for u (- , ) and aligned g(-u) & =2 ⁻¹ (e^ -u )- 2 & =2 ( ⁻¹ (e^u ) )- 2 & =2 ( 2 - ⁻¹ (e^u ) )- 2 & = 2 -2 ⁻¹ (e^u )=-g(u) aligned g(-u)=-g(u) g(u) is an odd function.