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 going to be using the given F of X and G of X functions to find the following composite function. So what we are asked to find is F divided by G of five. But before we find this composite function, we need to find the general form of this function which is F divided by G of X. Now F divided by G of X can be rewritten as F of X divided by G of X. And what this means is that we're going to be taking our given F of X function and dividing it by a given G of X function. So replacing F of X and G of X with the given functions is going to give us 25 X plus five divided by four X squared. So this is going to be the general form of the composite function that we're going to find. But what the composite function states is that now we want to find the value of the function with five as its input value. So we're going to be taking the value of five and replacing every X in our composite function with this value. And doing this is going to give us 25 times five Plus five in the numerator divided by four times 5 squared in the denominator. And now we just need to go ahead and simplify 25 times five is going to give us 125 and 1 25 plus three is going to give us 100 and 30 in the in the numerator Five squared is going to give us 25 in the denominator and times four is going to give us 100. So what we are left with is 130 divided by 100. But both of these values can be divided by 10. So if we divide the numerator and denominator by 10, what we are left with is 13/10, which is going to be the value of the composite function we are looking for. And with that being said, the answer to this problem is going to be a. 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.

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

Key Concepts

Function Notation

Composition of Functions

Evaluating Functions

Watch next