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BITSAT Mathematics Functions 2024 BITSAT 2024 (Memory Based Paper 1)

BITSAT Mathematics Question (2024) — Solution

Question

Let the function g:(- , ) (- 2 , 2 ) be given by g(u)=2 ^ -1 (e^u )- 2 . Then, g is

Options

  1. A. even and is strictly increasing in (0, )
  2. B. odd and is strictly decreasing in (- , )
  3. C. odd and is strictly increasing in (- , )
  4. D. neither even nor odd, but is strictly increasing in (- , )

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 (- , ).

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