00:01
This problem, we're given the functions for f of x and g of x.
00:03
So the first thing we're being asked to find is f of g of x.
00:06
So remember, when you're finding composites of functions, you always start with the inside function, which in this case is g of x, which means we really need to find f of one -third times x plus five.
00:18
Well, remember, what's in parentheses is your input.
00:21
So what we're going to do is substitute one -third times x plus five in place of x in our f function, which means we're going to have three times one -third times x plus five, and then we'll subtract five.
00:34
So now we just need to simplify.
00:36
Well, three times one -third is equal to one, which really just leaves us with x plus five minus five.
00:41
Well, five minus five is equal to zero, which means that these terms cancel and we're just left with x.
00:47
So what we've found is that f of g of x is simply just x.
00:50
Now, the second thing we want to do is find the opposite, at g of f of x.
00:55
So remember we always start with our inside function, which in this case is f of x...