Consider the function f( )=4 ( ^2 + ^4 ) Consider the following statements: 1. f( )=2 has no solution. 2. f ( )= 7 2 has a solution. Which of the above statements is/are correct?

Step-by-step solution

aligned f( )= & 4 ( ^2 + ^4 ) = & 4 ( ^2 + ^2 (1- ^2 ) ) = & 4 ( ^2 + ^2 - ^2 ^2 ) = & 4 (1- 1 4 ^2 2 ) & [ 2 =2 ] aligned aligned & f( )=2 & 4 (1- 1 4 ^2 2 )=2 & 1- 1 4 ^2 2 = 2 4 & - 1 4 ^2 2 =+ 1 2 -1 & - 1 4 ^2 2 =- 1 2 & ^2 2 =2 & 2 = 2 aligned Since cannot have vlaue greater than 1 & less than -1. Hence f( )=2 has no solution. aligned & f( )= 7 2 & 4 (1- 1 4 ^2 2 )= 7 2 & (1- 1 4 ^2 2 )= 7 8 aligned aligned & - 1 4 ^2 2 = 7 8 -1 & - 1 4 ^2 2 =- 1 8 & ^2 2 = 1 2 & 2 = 1 2 & 2 = 4 & 2 = ( / 4) & 2 = / 4 & =( )