00:01
Hi, here for the given question we are given that function f of x is equal to ceiling function x by 2.
00:08
Now here we need to find the value of f inverse of 4.
00:13
So here in our case we have f of x is equal to x by 2.
00:18
So here now we know that here f of x is equal to 4 has no solution because the largest possible value will be x.
00:30
So here in our case we can say that here the values of f of x are 0, 1, 2 and so on.
00:41
So here we have value of x by 2 is equal to k.
00:47
So here now we know that further there is no such integers, no such integer which satisfies x by 2 is equal to 4.
01:01
So here in our case we can say that the value of f inverse of 4 is an empty set.
01:11
So here this is for the first part of the question.
01:14
Now similarly for the second part of the question we need to find the value of f inverse of minus 4.
01:20
So here in our case now we know that these are the possible values and as we proved above here f of x is equal to minus 4 also has no solution because the smallest possible integer, smallest positive integer k which can be written as ceiling function x by 2 of k, k is equal to 1 and here there is no such integers that exist, no such integer such that ceiling function of x by 2 is equal to minus 4...