Let i be a function from the set A to the set B. Let Sbe a subset of E. We defin
ID: 3146052 • Letter: L
Question
Let i be a function from the set A to the set B. Let Sbe a subset of E. We define the inverse image of S to be the subset of A whose lements are precisely all pre-images of all elements of S. We denote the inverse image of S by (S),soSHOEAlKa)ES Beware: The notation is used in two different ways. Do not confuse the notation introduced here with the notation) for the value at y of the inverse of the invertible function f. Notice also that (S, the inverse image of the set S, makes sense for all functions 1, not just invertible functions.) Let i be the function from R to R defined by (x). Find 31. Required information 32. Required informationExplanation / Answer
Hi,
As defined in the question, f-1 is defined as the set of elements with pre images defined by the function x2,
1. In this the interval is given as 0<x<1 ,i,e we need to find the interval of x where x2 falls in this interval,
which is -1 to 1, now the value could either be negative of positive, since we are suaring it, it could be both ways,
so the interval will be
-1<x<0 v 0<x<1 i.e the second option.
2. Similar to the above part, if x>4, implies the value can be >2 like 3,4 or -3,-4 since squaring them resultls in >4 value, hence the answer is x>2 v x<-2 i,e first option
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