BITSAT2024MathematicsFunctionsActual
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
Given that g(u)=2 ⁻¹ (e^u )- 2 g(-u)=2 ⁻¹ (e^ -u )- 2 =2 ⁻¹ ( 1 e^u )- 2 =2 ⁻¹ (e^u )- 2 =2 [ 2 - ⁻¹ (e^u ) ]- 2 = -2 ⁻¹ (e^u )- 2 = 2 -2 ⁻¹ (e^u )=-g(u) g is an odd function. Also g^ (u)= 2 e^u 1+e^ 2 u 0, u (- , ) g is strictly increasing on (- , ) .