In Exercises 91–94, use the graphs of f and g to evaluate each co...

Question

In Exercises 91–94, use the graphs of f and g to evaluate each composite function.

Graph showing functions f(x) in red and g(x) in blue for composite function evaluation.

(fog) (-1)

Accepted Answer

Hey everyone in this problem we are asked to evaluate the following composite functions using the graphs of FNG that were given. And we're asked to find f of G of -3. Okay. Alright. So let's start with what actually is F G of negative three. Okay, well this is a composite function. Okay. And we can write it as a following F Of G of -3. OK, recall these are equivalent. How can we evaluate this? Okay, so we want to take F and we want to evaluate it at G of negative three. Okay. We don't know what Gm negative three is right this second. So we can evaluate this outer function F. Okay, so let's work from the inside out. We can do is we can find G of three. Sorry, negative three. G F negative three. Case of honor graph here we have the function G in blue at negative three. That means when x is negative three. Is we have negative one, negative two, negative three. We go down till we see this blue line and so G a negative three is going to be negative three. So now we have F at G F negative three which we know is negative three. Well now we just have a function evaluation like normal. We have f evaluated at negative three. We know how to do that. Okay, we have the function F in red. If we take this at X equals negative three. Negative one, negative two, negative three. And we go straight up until we hit that function we're gonna be here At five. So effort -3 is equal to five. Okay, so the composition of the function, we just write F. Of G. Of negative three and then we work from the inside. Find that inside value work our way out. And what we found is that the Composite function is evaluated to five. Okay. So we have answer d. Five. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 91–94, use the graphs of f and g to evaluate each composite function.
(fog) (-1)

Key Concepts

Composite Functions

Function Evaluation from Graphs

Interpreting Graphs of Functions

Watch next