The number of solutions of the equation (2x) + (2 - 2 ) (x) + 2 - 1 = 0 in the interval x [- , 3 ] is equal to:

Step-by-step solution

Using the identity (2x) = 1 - 2 ^2(x) , the given equation becomes: 1 - 2 ^2(x) + (2 - 2 ) (x) + 2 - 1 = 0 -2 ^2(x) + (2 - 2 ) (x) + 2 = 0 2 ^2(x) - (2 - 2 ) (x) - 2 = 0 Factorizing the quadratic equation: 2 ^2(x) - 2 (x) + 2 (x) - 2 = 0 2 (x)( (x) - 1) + 2 ( (x) - 1) = 0 (2 (x) + 2 )( (x) - 1) = 0 This gives (x) = 1 or (x) = - 1 2 . Now, we find the number of solutions in the interval [- , 3 ] . For (x) = 1 : In [- , 3 ] , the solutions are x = 2 and x = 5 2 . (2 solutions) For (x) = - 1 2 : In [- , 0] , the solut