Simplifying the Composite Function

Oct 13, 2025 by miodeya.com 140 views

**Composite Functions: A Simplified Expression** =====================================================

What is a Composite Function?

A composite function is a function that is derived from two or more functions. It is a function of a function, where the output of one function is used as the input for another function. In this article, we will explore how to simplify a composite function using two given functions, H(x) and J(x).

Given Functions

We are given two functions:

H(x) = -9x + 4
J(x) = -3x - 6

The Composite Function

The composite function (H * J)(x) is defined as:

(H * J)(x) = H(J(x))

Substituting the given functions, we get:

(H * J)(x) = H(-3x - 6)

Simplifying the Composite Function

To simplify the composite function, we need to substitute the expression for J(x) into the function H(x). This means we replace x with -3x - 6 in the function H(x).

(H * J)(x) = -9(-3x - 6) + 4

Expanding and Simplifying

Now, let's expand and simplify the expression:

(H * J)(x) = -9(-3x - 6) + 4 = 27x + 54 + 4 = 27x + 58

Conclusion

The simplified expression for the composite function (H * J)(x) is 27x + 58.

Q&A

Q: What is a composite function?

A: A composite function is a function that is derived from two or more functions. It is a function of a function, where the output of one function is used as the input for another function.

Q: How do we simplify a composite function?

A: To simplify a composite function, we need to substitute the expression for one function into the other function.

Q: What is the simplified expression for the composite function (H * J)(x)?

A: The simplified expression for the composite function (H * J)(x) is 27x + 58.

Q: What are the given functions?

A: The given functions are H(x) = -9x + 4 and J(x) = -3x - 6.

Q: How do we substitute the expression for J(x) into the function H(x)?

A: We replace x with -3x - 6 in the function H(x).

Q: What is the final expression after expanding and simplifying?

A: The final expression after expanding and simplifying is 27x + 58.

Q: What is the correct answer for the simplified expression of the composite function (H * J)(x)?

A: The correct answer is 27x + 58.

Q: What are the possible answers for the simplified expression of the composite function (H * J)(x)?

A: The possible answers are A. 27x^2 + 42x - 24, B. 27x + 58, C. 27x - 18, and D. -12x - 18.

Q: Which of the possible answers is correct?

A: The correct answer is B. 27x + 58.

Q: Why is B. 27x + 58 the correct answer?

A: B. 27x + 58 is the correct answer because it is the simplified expression for the composite function (H * J)(x) after substituting the expression for J(x) into the function H(x) and expanding and simplifying the expression.

Q: What is the final answer for the simplified expression of the composite function (H * J)(x)?

A: The final answer is 27x + 58.