Given F ( X ) = 10 − 2 X F(x) = 10 - 2x F ( X ) = 10 − 2 X , Find F ( 7 F(7 F ( 7 ].A. -4 B. 3 C. 7 D. 56

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Introduction

In mathematics, functions are used to describe the relationship between variables. Given a function f(x), we can find the value of the function at a specific point x by plugging in the value of x into the function. In this article, we will learn how to find the value of a function using a given function f(x) = 10 - 2x.

Understanding the Function

The given function is f(x) = 10 - 2x. This function takes a value of x and returns a value of f(x). To find the value of f(x), we need to substitute the value of x into the function.

Substituting the Value of x

To find the value of f(7), we need to substitute x = 7 into the function f(x) = 10 - 2x.

Step 1: Substitute x = 7 into the Function

f(7) = 10 - 2(7)

Step 2: Simplify the Expression

To simplify the expression, we need to multiply 2 and 7.

f(7) = 10 - 14

Step 3: Combine Like Terms

Now, we can combine the like terms.

f(7) = -4

Conclusion

In this article, we learned how to find the value of a function using a given function f(x) = 10 - 2x. We substituted x = 7 into the function and simplified the expression to find the value of f(7). The final answer is -4.

Discussion

  • What is the value of f(7) if f(x) = 3x - 2?
  • How do you find the value of a function using a given function?
  • What is the difference between a function and an equation?

Answer Key

  • A. -4
  • B. 3
  • C. 7
  • D. 56

Step-by-Step Solution

  1. Substitute x = 7 into the function f(x) = 10 - 2x.
  2. Simplify the expression by multiplying 2 and 7.
  3. Combine like terms to find the value of f(7).

Example Problems

  1. Find the value of f(5) if f(x) = 2x + 3.
  2. Find the value of f(3) if f(x) = x^2 - 2x.
  3. Find the value of f(2) if f(x) = 3x - 1.

Tips and Tricks

  • Always substitute the value of x into the function.
  • Simplify the expression by combining like terms.
  • Use the order of operations (PEMDAS) to simplify the expression.

Common Mistakes

  • Not substituting the value of x into the function.
  • Not simplifying the expression by combining like terms.
  • Not using the order of operations (PEMDAS) to simplify the expression.

Real-World Applications

  • Finding the value of a function is used in many real-world applications, such as physics, engineering, and economics.
  • Understanding functions is essential in many fields, such as computer science, data analysis, and machine learning.

Conclusion

In conclusion, finding the value of a function is a crucial concept in mathematics. By following the steps outlined in this article, you can find the value of a function using a given function. Remember to substitute the value of x into the function, simplify the expression by combining like terms, and use the order of operations (PEMDAS) to simplify the expression.

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Q&A: Finding the Value of a Function

Q: What is the value of f(7) if f(x) = 10 - 2x?

A: To find the value of f(7), we need to substitute x = 7 into the function f(x) = 10 - 2x. This gives us f(7) = 10 - 2(7) = 10 - 14 = -4.

Q: How do you find the value of a function using a given function?

A: To find the value of a function, we need to substitute the value of x into the function and simplify the expression by combining like terms.

Q: What is the difference between a function and an equation?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). An equation is a statement that two expressions are equal. A function can be represented by an equation, but not all equations represent functions.

Q: Can you give an example of a function?

A: Yes, f(x) = 2x + 3 is a function. It takes a value of x and returns a value of f(x).

Q: Can you give an example of an equation that is not a function?

A: Yes, x^2 + 2x - 3 = 0 is an equation that is not a function. It is a quadratic equation that has two solutions, but it does not represent a function.

Q: How do you determine if an equation represents a function?

A: To determine if an equation represents a function, we need to check if the equation passes the vertical line test. If the equation passes the vertical line test, then it represents a function.

Q: What is the vertical line test?

A: The vertical line test is a test used to determine if an equation represents a function. To perform the vertical line test, we draw a vertical line on the graph of the equation. If the line intersects the graph at more than one point, then the equation does not represent a function.

Q: Can you give an example of a function that passes the vertical line test?

A: Yes, f(x) = 2x + 3 is a function that passes the vertical line test. Its graph is a straight line that passes the vertical line test.

Q: Can you give an example of a function that does not pass the vertical line test?

A: Yes, f(x) = x^2 is a function that does not pass the vertical line test. Its graph is a parabola that does not pass the vertical line test.

Q: How do you find the value of a function at a specific point?

A: To find the value of a function at a specific point, we need to substitute the value of x into the function and simplify the expression by combining like terms.

Q: Can you give an example of finding the value of a function at a specific point?

A: Yes, to find the value of f(5) if f(x) = 2x + 3, we need to substitute x = 5 into the function f(x) = 2x + 3. This gives us f(5) = 2(5) + 3 = 10 + 3 = 13.

Conclusion

In conclusion, finding the value of a function is a crucial concept in mathematics. By following the steps outlined in this article, you can find the value of a function using a given function. Remember to substitute the value of x into the function, simplify the expression by combining like terms, and use the order of operations (PEMDAS) to simplify the expression.

Tips and Tricks

  • Always substitute the value of x into the function.
  • Simplify the expression by combining like terms.
  • Use the order of operations (PEMDAS) to simplify the expression.
  • Check if the equation passes the vertical line test to determine if it represents a function.

Common Mistakes

  • Not substituting the value of x into the function.
  • Not simplifying the expression by combining like terms.
  • Not using the order of operations (PEMDAS) to simplify the expression.
  • Not checking if the equation passes the vertical line test to determine if it represents a function.

Real-World Applications

  • Finding the value of a function is used in many real-world applications, such as physics, engineering, and economics.
  • Understanding functions is essential in many fields, such as computer science, data analysis, and machine learning.

Conclusion

In conclusion, finding the value of a function is a crucial concept in mathematics. By following the steps outlined in this article, you can find the value of a function using a given function. Remember to substitute the value of x into the function, simplify the expression by combining like terms, and use the order of operations (PEMDAS) to simplify the expression.