 ### Evaluating composite functions: using graphs | Mathematics III | High School Math | Khan Academy

– So we have the graphs
of two functions here. We have the graph y equals f of x and we have the graph
y is equal to g of x. And what I wanna do in this video is evaluate what g of, f of, let me do the f of it another color, f of negative five is,
f of negative five is. And it can sometimes
seem a little daunting when you see these composite functions. You’re evaluating the function
g at f of negative five. What does all this mean? We just have to remind ourselves what functions are all about. They take an input and
they give you an output. So really, what we’re doing is we’re going to take, we have the function f. We have the function f. We’re going to input negative
five into that function. We’re going to input negative five into that function and
it’s going to output f of negative five. It’s going to output f of negative five and we can figure what that is. And then that’s going to be the input into the function g. So that’s going to be the
input into the function g and so we’re going to, and then the output is going
to be g of f of negative five, g of f of negative five. Let’s just do it step by step. So the first thing we wanna figure out is what is the function f when
x is equal to negative five? What is f of negative five? Well we just have to see when
x is equal to negative five. When x is equal to negative five, the function is right over here. Let’s see, let me see if I
can draw a straight line. So then x is equal to negative five. The function is right over here. It looks like f of negative
five is equal to negative two. It’s equal to negative two. You see that right over there. So, f of negative five is negative two. And so we can now think of this instead of saying g of f of negative five, we could say well f of negative
five is just negative two, is just negative two. So this is going to be
equivalent to g of negative two, g of negative two, g of negative two. We’re gonna take negative two into g and we’re gonna output g of negative two. So we’re taking that output, negative two and we’re inputting into g. So when x is negative two, when x is negative two, what is g? So we see, when x is negative two, g, the graph is right over there, g of negative two is one. So this is going to be one. So g of f of negative five
sounds really complicated, we were able to figure out is one ’cause you input negative five into f, it outputs negative two. And then you input negative
two into g, it outputs one and we’re all done.