If 𝑓 of 𝑥 equals three minus 𝑥 squared and 𝑔 of 𝑥 equals two 𝑥 plus four, find 𝑓 of 𝑔 of one.
What we’re doing is we’re completing the composition of functions. So we can rewrite this in a way that might make a little more sense. It can be written as 𝑓 of 𝑔 of one. It’s said the same way, but written a little bit differently. So essentially, we plug one into the 𝑔 function, and then whatever we get for that, we will take that number and plug it into the 𝑓 function.
So first, let’s plug one into the 𝑔 function for 𝑥. So instead of two 𝑥 plus four, it’s two times one plus four; we’re plugging in one. And two times one is two plus four is six. So now we’re gonna plug six into the 𝑓 of 𝑥 function, so we have three minus six squared, and three minus 36 is equal to negative 33.