Without using paper and pencil, evaluate each expression given th...

Question

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2
(ƒ∘g)(2)

Accepted Answer

Hello, today we're gonna be using the given F of X and G of X function to find the following composite function. So what we are asked to find is f of G of four and F of G of four can be rewritten as F of X with G F four as its input value. So what does this mean exactly? Well, what this means is we're going to be taking our G of X function which is four X squared and plugging in four as the input value for X, then whatever value we get from this function is going to act as the input value for F of X function. So in order to start this problem, let's go ahead and first find our G of four value. So we know that our G of X function is four X squared. But since we're plugging in four for our value of X, we're gonna be replacing X with four and that's going to give us four times four squared. And now we just need to go ahead and simplify Four squared is going to give us 16. So we have four times 16 and four times 16. Is going to give us the value of 64. So we know that GF four is equal to 64. So we're going to be taking this value of 64 and replacing GF four with 64 in our composite function. And that's going to give us f of 64. Now, F of 64 means that we're going to be taking our F of X function which is two X plus five. And since 64 is going to be the input value for X value here, we're going to be replacing X with 64. And that's going to leave us with two times 64 plus five and two times 64 is going to give us the value of 128 plus five is going to give us 133. So f of 64 is equal to 133, which is going to be the value of the composite function we're looking for. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ∘g)(2)