Suppose $f(x) = 14x - 2$. Calculate $f(x-3) + F(3x$\]. $\square$

Suppose $f(x) = 14x - 2$. Calculate $f(x-3) + f(3x)$

Introduction

In this article, we will explore the concept of function composition and how it can be used to simplify complex mathematical expressions. We will start by defining a function $f(x)$ and then use it to calculate the value of $f(x-3) + f(3x)$. This problem requires a deep understanding of function notation and the ability to apply it to solve a mathematical expression.

Understanding Function Notation

Before we dive into the problem, let's take a moment to understand function notation. A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is typically denoted by a letter, such as $f$, and is defined by a formula that takes an input and produces an output. In this case, the function $f(x)$ is defined as $14x - 2$.

Calculating $f(x-3)$

To calculate $f(x-3)$, we need to substitute $x-3$ into the formula for $f(x)$. This means that we will replace every instance of $x$ in the formula with $x-3$. So, we get:

$f(x-3) = 14(x-3) - 2$

Expanding the formula, we get:

$f(x-3) = 14x - 42 - 2$

Simplifying the expression, we get:

$f(x-3) = 14x - 44$

Calculating $f(3x)$

To calculate $f(3x)$, we need to substitute $3x$ into the formula for $f(x)$. This means that we will replace every instance of $x$ in the formula with $3x$. So, we get:

$f(3x) = 14(3x) - 2$

Expanding the formula, we get:

$f(3x) = 42x - 2$

Calculating $f(x-3) + f(3x)$

Now that we have calculated $f(x-3)$ and $f(3x)$, we can add them together to get the final result. So, we get:

$f(x-3) + f(3x) = (14x - 44) + (42x - 2)$

Combining like terms, we get:

$f(x-3) + f(3x) = 56x - 46$

Conclusion

In this article, we have explored the concept of function composition and how it can be used to simplify complex mathematical expressions. We have defined a function $f(x)$ and used it to calculate the value of $f(x-3) + f(3x)$. The final result is $56x - 46$. This problem requires a deep understanding of function notation and the ability to apply it to solve a mathematical expression.

Final Answer

The final answer is $\boxed{56x - 46}$.

Related Topics

• Function notation
• Function composition
• Algebraic expressions
• Mathematical problem-solving

References

• [1] "Function Notation" by Khan Academy
• [2] "Function Composition" by Math Open Reference
• [3] "Algebraic Expressions" by Purplemath
  Suppose $f(x) = 14x - 2$. Calculate $f(x-3) + f(3x)$

Q&A: Calculating $f(x-3) + f(3x)$

In this article, we will answer some common questions related to calculating $f(x-3) + f(3x)$.

Q: What is the formula for $f(x-3)$?

A: The formula for $f(x-3)$ is $14(x-3) - 2$. This is obtained by substituting $x-3$ into the formula for $f(x)$.

Q: What is the formula for $f(3x)$?

A: The formula for $f(3x)$ is $14(3x) - 2$. This is obtained by substituting $3x$ into the formula for $f(x)$.

Q: How do I calculate $f(x-3) + f(3x)$?

A: To calculate $f(x-3) + f(3x)$, you need to add the two formulas together. This means combining like terms and simplifying the expression.

Q: What is the final result of $f(x-3) + f(3x)$?

A: The final result of $f(x-3) + f(3x)$ is $56x - 46$. This is obtained by combining like terms and simplifying the expression.

Q: What is the significance of function notation in this problem?

A: Function notation is used to define the function $f(x)$ and to substitute values into the formula. It is an essential concept in mathematics and is used to represent functions in a concise and clear way.

Q: How can I apply this concept to other problems?

A: This concept can be applied to other problems by substituting values into the formula and combining like terms. It is essential to understand function notation and how to apply it to solve mathematical expressions.

Q: What are some common mistakes to avoid when calculating $f(x-3) + f(3x)$?

A: Some common mistakes to avoid when calculating $f(x-3) + f(3x)$ include:

• Not substituting the correct values into the formula
• Not combining like terms correctly
• Not simplifying the expression correctly

Q: How can I practice and improve my skills in calculating $f(x-3) + f(3x)$?

A: You can practice and improve your skills in calculating $f(x-3) + f(3x)$ by:

• Working through multiple examples and exercises
• Practicing with different values and formulas
• Reviewing and understanding the concept of function notation

Conclusion

In this article, we have answered some common questions related to calculating $f(x-3) + f(3x)$. We have discussed the formula for $f(x-3)$ and $f(3x)$, how to calculate $f(x-3) + f(3x)$, and the significance of function notation in this problem. We have also provided some tips and advice on how to practice and improve your skills in calculating $f(x-3) + f(3x)$.

Final Answer

The final answer is $\boxed{56x - 46}$.

Related Topics

• Function notation
• Function composition
• Algebraic expressions
• Mathematical problem-solving

References

• [1] "Function Notation" by Khan Academy
• [2] "Function Composition" by Math Open Reference
• [3] "Algebraic Expressions" by Purplemath