00:01
In this problem, we're given two functions.
00:02
F of x equals x squared plus 1, and g of x equals x minus 3.
00:08
So we have four parts of this problem.
00:10
In the first part, part a, we need to solve for f composed of g of 1.
00:24
So our function is composition function f composed of g at an input value of 1.
00:29
You know this equals f of g of 1 in the inside with f of the 1.
00:37
On the outside.
00:40
So this equals f of g of one being one minus three.
00:49
So now we get this to equal f of negative two.
00:53
Oops, let me write that in red.
00:58
F of negative two because g of one has an output of negative two.
01:05
And now the input for f is negative two.
01:12
So f of negative two equals negative two squared plus 1, which equals 4 plus 1, which equals 5.
01:27
F composed of g of 1 equals 5.
01:30
Scroll down to part b.
01:36
Part b is what is g composed of f of 1.
01:45
So similar to part a, but now our roles of the functions are reversed...