The Function $g$ Is Defined As $g(x) = 2x^2 + 4x$. Find $g(x-6$\]. Write Your Answer Without Parentheses, And Simplify It As Much As Possible.$g(x-6) = $ $\square$

Introduction

In this article, we will explore the concept of function composition and how it can be used to simplify expressions. We will focus on the function $g(x) = 2x^2 + 4x$ and find the expression for $g(x-6)$.

Understanding Function Composition

Function composition is a fundamental concept in mathematics that involves combining two or more functions to create a new function. In this case, we want to find the expression for $g(x-6)$, which involves substituting $(x-6)$ into the function $g(x)$.

Step 1: Substitute (x-6) into the Function g(x)

To find the expression for $g(x-6)$, we need to substitute $(x-6)$ into the function $g(x) = 2x^2 + 4x$. This means that we will replace every instance of $x$ in the function with $(x-6)$.

Step 2: Simplify the Expression

After substituting $(x-6)$ into the function, we need to simplify the expression. This involves expanding and combining like terms.

The Expression for g(x-6)

Let's start by substituting $(x-6)$ into the function $g(x) = 2x^2 + 4x$.

g(x-6) = 2(x-6)^2 + 4(x-6)

Now, let's simplify the expression by expanding and combining like terms.

g(x-6) = 2(x^2 - 12x + 36) + 4(x-6)

Next, we need to distribute the 2 and 4 to the terms inside the parentheses.

g(x-6) = 2x^2 - 24x + 72 + 4x - 24

Now, let's combine like terms.

g(x-6) = 2x^2 - 20x + 48

Conclusion

In this article, we have explored the concept of function composition and how it can be used to simplify expressions. We have focused on the function $g(x) = 2x^2 + 4x$ and found the expression for $g(x-6)$. By substituting $(x-6)$ into the function and simplifying the expression, we have arrived at the final expression for $g(x-6)$.

Final Answer

The final expression for $g(x-6)$ is:

$2x^2 - 20x + 48$

Introduction

In our previous article, we explored the concept of function composition and how it can be used to simplify expressions. We focused on the function $g(x) = 2x^2 + 4x$ and found the expression for $g(x-6)$. In this article, we will answer some common questions related to the function $g(x-6)$.

Q: What is the function g(x-6)?

A: The function $g(x-6)$ is a simplified expression that represents the value of the function $g(x)$ when the input is $(x-6)$. It is obtained by substituting $(x-6)$ into the function $g(x) = 2x^2 + 4x$ and simplifying the expression.

Q: How do I find the expression for g(x-6)?

A: To find the expression for $g(x-6)$, you need to substitute $(x-6)$ into the function $g(x) = 2x^2 + 4x$ and simplify the expression. This involves expanding and combining like terms.

Q: What is the final expression for g(x-6)?

A: The final expression for $g(x-6)$ is:

$2x^2 - 20x + 48$

This expression represents the value of the function $g(x)$ when the input is $(x-6)$.

Q: Can I use the expression for g(x-6) to find the value of g(x) for any input?

A: Yes, you can use the expression for $g(x-6)$ to find the value of $g(x)$ for any input. Simply substitute the input value into the expression and evaluate it.

Q: What is the domain of the function g(x-6)?

A: The domain of the function $g(x-6)$ is all real numbers, since the expression $2x^2 - 20x + 48$ is defined for all real values of $x$.

Q: Can I graph the function g(x-6)?

A: Yes, you can graph the function $g(x-6)$ by plotting the expression $2x^2 - 20x + 48$ on a coordinate plane.

Q: What is the range of the function g(x-6)?

A: The range of the function $g(x-6)$ is all real numbers, since the expression $2x^2 - 20x + 48$ can take on any real value.

Conclusion

In this article, we have answered some common questions related to the function $g(x-6)$. We have provided the final expression for $g(x-6)$ and discussed its domain, range, and graph.

Final Answer

The final expression for $g(x-6)$ is:

$2x^2 - 20x + 48$

This expression represents the value of the function $g(x)$ when the input is $(x-6)$.