Let f(x)= x x ;(x 1) Consider the following statements: 1. f(x) is increasing in the interval (e, ) 2. f(x) is decreasing in the interval (1, e) 3. 9 7 7 9 Which of the statements given above are correct?

Step-by-step solution

aligned & f(x)= x (x) (x 1) & f(x)= x-1 [ (x)]^2 aligned f(x) is + ve , x (e, ) (1) is correct f(x) is -ve x (1, e) (2) is correct As x is an increasing function aligned 7^9 & 9^7 7^9 & 9^7 9 7 & 7 9 aligned statement (3) is correct Hence, statements (1), (2) and (3) are correct.