Composite functions
Let ƒ(x) = x³, g (x) = sin x an...

Question

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.

Find the domain of g o ƒ.

Accepted Answer

Welcome back everyone. In this problem, for the functions f of x equals cosine x and g of x equals x to the 5th power, we want to determine the domain of the composite function g of f. For our answer choices, a is open parenthesis negative infinity infinity closed parenthesis. B is open parenthesis negative infinity zero closed parenthesis. C is open parenthesis, 0, infinity, closed parenthesis, and d is open bracket, 0, infinity, closed parenthesis. Now we want to determine the domain of the composite function. So first, we need to figure out what that composite function is. Now recall that the composition of g of f means that we're putting the function f of x into the function g evaluating the innermost function first. So that means in our function g of x, wherever we see x, no, we're going to put f of x. So that tells us then that g of f of x would be equal to not x to the 5th, but the cosine of x raised to the 5th power. Now, we can rewrite that this way where our power of 5 comes right after the cosine, but it's saying the same thing. The cosine of x raised to the 5th power. Now we want to determine the domain of our composite function and the simplified composite function has no domain constraints or undefined points. In other words, our input constraints or undefined points. In other words, our input value x is a real number. So, therefore, that means the domain is the set of all real numbers starting from negative infinity all the way to infinity. That tells us then that our answer would be answer choice a. Open parenthesis negative infinity and infinity closed parenthesis. Thanks a lot for watching everyone. I hope this video helped.

Composite functions
Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.
Find the domain of g o ƒ.

Key Concepts

Composite Functions

Domain of a Function

Function Behavior and Restrictions

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