00:01
Alright, in this problem we're given two functions, but the one that's important here to answer this problem in this video is using f of x.
00:11
So we're given the function f of x equals 1 half x minus 4.
00:16
And we're asked to calculate f of f of 1 of 8.
00:20
So this is what you call composition of functions.
00:22
We're having to calculate the value, evaluate the function at two different values.
00:28
And we're going to start with the inner function evaluation.
00:32
So we're going to start from inwards and using that answer we're going to use the outer.
00:36
So that means the last one.
00:38
So let's go ahead and calculate f of 1 of 8 first.
00:44
In order to do this we have to take the function f of x given to us and replace the x value.
00:49
Remember this is an x value that was replaced.
00:51
So we're going to write 1 half and instead of x we write times 1 eighth minus 4.
00:58
You want to go ahead and calculate 1 half times 1 eighth.
01:03
We know that's 1 16 subtracted by 4.
01:07
And in order to be able to subtract this we have to change 4 to have a denominator of 16.
01:15
So that means we're going to, i'll do it on the side, 4 over 1.
01:21
We want to multiply by 16 top and bottom to give us an equivalent fraction of 64 over 16.
01:31
That's equivalent to 4 over 1.
01:33
So i'm going to replace that into this function 1 over 16 minus 64 over 16.
01:41
And that's going to give us an answer of negative 63 over 16.
01:47
So this was remember f of 1 eighth that we just evaluated.
01:52
So this is important.
01:54
We're going to use this answer, negative 63 over 16 and replace it again into this function f of x.
02:04
They want us to calculate it twice, do two evaluations...