00:01
Okay, so this question we want to see if various functions are onto or not.
00:05
So first up we have a f of n is equal to n minus 1.
00:12
So this is a onto function because if we set n as m plus 1 where m is your is an integer, then f of m plus 1 is equal to m plus 1 minus 1.
00:30
So this is and m is your integers.
00:34
So we can get the set of all integers just by writing n is m plus one.
00:39
So therefore this is an onto function.
00:45
Now b, f of n is equal to n squared plus one.
00:50
So this is pretty clearly not an onto function because you have n squared is greater than or equal to zero.
00:57
So because you're adding one to this, it follows that n squared plus one or f of n is going to be greater than or f of n is going to be greater than.
01:03
Then or equal to 1.
01:04
But your set of integers contains negative numbers.
01:08
You have 0 or minus 1, 1, minus 2, 2, and so on and so on...