If the domain of the function f(x)= _e ( 2 x-3 5+4 x )+ ⁻¹ ( 4+3 x 2-x ) is [ , ) then ^2+4 is equal to

Step-by-step solution

Given function is f(x)= _e ( 2 x-3 5+4 x )+ ⁻¹ ( 4+3 x 2-x ) For domain, the conditions are 2 x-3 5+4 x 0 and | 4+3 x 2-x | 1 Now, 2 x -3 5+4 x 0 x (- ,- 5 4 ) [ 3 2 , ) and -1 4+3 x 2-x 1 (-1 4+3 x 2-x ) ( 4+3 x 2-x 1 ) ( 6+2 x 2- x 0 ) ( 2+4 x 2- x 0 ) aligned & 6+2 x 2-x 2+4 x 2-x 0 & x [-3,- 1 2 ] aligned Hence, we get the domain of f as x [-3,- 5 4 ) This means that =-3, =- 5 4 Thus, ^2+4 =9-5=4