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(g∘ƒ)(2)

Accepted Answer

Hello, today we're going to be using the given F of X and G of X function to find the following composite function. So what the composite function states is that we have g of f of four and G of F of four can be rewritten as the function G of X with F of four as its input value. So what this means is we're going to be taking our F of X function plugging in for, into this function and whatever value that we get from the function is going to be the input value for G of X function. So let's go ahead and start this by finding F of four. Now, we know that F of X is equal to two X plus five, but F of four states that four is going to be the input value for X. So we're going to be replacing X with four in this function. And what we are left with is two times four plus five. Now simplifying this two times four is going to give us eight And 8-plus 5 is going to give us the value of 13. So we know that f of four is equal to 13. So we're gonna go ahead and replace f of four in our composite function with 13. And what this leaves us with is G of 13. And now we're gonna be taking our G of X function, which in this case is four X squared and we're going to be replacing X with the value of 13. And doing this is going to leave us with four times squared. Now, we just need to go ahead and simplify 13 squared is going to give us the value Of 169. So we have four times 169, which is going to give us the value of 676. And this is going to be the value of the composite function that we are looking for. And with that being said, the answer to this problem is going to be c 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(g∘ƒ)(2)

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