Let f(x) = - x be a function defined on R , where and are positive constants. If the range of f(x) is [ 1 3 , 1 ] , then the value of 3 + 2 is equal to :

Step-by-step solution

We know that for any real x , x [-1, 1] . Therefore, the denominator - x lies in the interval [ - 1, + 1] . Since > 0 and > 0 , and the range contains only positive values, we must have - 1 > 0 , which means > 1 . The maximum value of the function occurs when the denominator is minimum: f_ = - 1 = 1 = - 1 The minimum value of the function occurs when the denominator is maximum: f_ = + 1 = 1 3 3 = + 1 Substituting = - 1 into the second equation: 3( - 1) = + 1 3 - 3 = + 1 2 = 4 = 2 Using = 2 , we get = 2 - 1 = 1 . Fi