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Current time:0:00Total duration:3:02

Video transcript

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 want to do in this video is evaluate what G of f of F let me do the F of in another color F of negative five is f of negative five is and it can sometimes see a little daunting when you see these composite functions you're taking you're evaluating the function G at F of negative five what does all of this mean you 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 we could 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 want to 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 when 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 2 G of negative 2 we're going to take negative 2 into G and we're going to output G of negative 2 so we're taking that output negative 2 and we're inputting into G so when X is negative 2 when X is negative 2 what is G so we see when X is negative 2 G the graph is right over there G of negative 2 is is 1 so this is going to be 1 so at G of F of negative 5 sounds really complicated we were able to figure out is 1 because you input negative 5 into f it outputs negative 2 and then you input negative 2 into G it outputs 1 and we're all done