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 .

Evaluate h(g( π/2)).

Accepted Answer

Welcome back, everyone. In this problem, we want to evaluate the composite function of B of A of a third of pi, given that a of x equals the cosine of x and a b of x equals the square root of x for our answer choices. A is the square root of 2 divided by 2. B is the square root of 2. C is a half and d is 1. Now if we're evaluating a composite function, recall that generally, if we have a composite function, let's say g of f of x, it means that we're putting f of x, right, into the function g of x. In other words, we're going to evaluate our innermost function first and then put it into our parent function. In this case, we're putting b we're putting a of a third of pi into b. So we can evaluate a of a third of pi first and then put it into our function b. So let's go ahead and do that. Now we know that a of x equals the cosine of x. So that means a of a third of Pi would be equal to the cosine of a third of Pi. Now we know that the cosine of a third of Pi is a half. So that would be a of a third of Pi. And now we have our value for a of a third of Pi. That means we can substitute it into our function for b. So this tells us then that b of a of a third of Pi is going to be b of a half since a of a third of Pi is a half. So we have our function b of x equals the square root of x. So that means b of a half would be equal to the square root of a half. Let's go ahead and simplify. Now we can also recall recall that the square root of a quotient is the same thing as the square root of its numerator divided by the square root of its denominator. So we can rewrite the square root of a half as the square root of 1 which is which equals 1. So I can just write 1 divided by the square root of 2. To simplify even further, we can rationalize our fraction which means multiplying both the numerator and the denominator by the square root of 2 and 1 multiplied by the square root of 2 equals the square root of 2. While the square root of 2 multiplied by the square root of 2 equals 2. Therefore, this tells us that b of a of a third of pie would be equal to the square root of 2 divided by 2. When we look back at our answer choices, that would have been answer choice a. 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 .
Evaluate h(g( π/2)).

Key Concepts

Composite Functions

Function Evaluation

Trigonometric Functions

Watch next