00:01
This problem gives us a pair of functions, f of x equal to x squared plus 4, and g of x plus 5, and we want to find two function compositions, first f of g of x and then g of x.
00:11
And when we're doing function compositions, remember that what we're doing is taking one function and treating it as the input of the other function.
00:18
So for f of g of x, what this is telling us to do is to take the entire g of x function, which is x plus 5, and replace x in f of x and evaluate.
00:28
So f of g of x will be equal to the x plus five value for g of x, replacing x and x squared plus four.
00:37
So x plus five squared still plus four.
00:40
And now we can simplify by multiplying x plus five by x plus five, which will give us x squared, and then five x and five x to give us 10x, and then five times five to give us 25, still plus four.
00:53
And the last thing we need to do to evaluate there is combine our constants, 25 and four, which gives us x, squared plus 10x plus 29...