Find The Value Of $g(25)$ For The Function Below:$g(x) = 24(x - 39)$A. 561 B. 311 C. -18 D. 336

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Introduction

In mathematics, functions are a fundamental concept that helps us describe relationships between variables. Given a function, we can find its value for a specific input by substituting the input into the function and performing the necessary calculations. In this article, we will explore how to find the value of a function for a given input, using the function g(x)=24(x−39)g(x) = 24(x - 39) as an example.

Understanding the Function

The function g(x)=24(x−39)g(x) = 24(x - 39) is a linear function, which means it has a constant rate of change. The function takes an input xx and returns an output g(x)g(x), which is calculated by multiplying the input by 24 and then subtracting 39 times 24.

Finding the Value of the Function

To find the value of the function g(x)g(x) for a given input, we need to substitute the input into the function and perform the necessary calculations. In this case, we want to find the value of g(25)g(25).

Step 1: Substitute the Input into the Function

To find the value of g(25)g(25), we need to substitute x=25x = 25 into the function g(x)=24(x−39)g(x) = 24(x - 39).

g(25) = 24(25 - 39)

Step 2: Perform the Calculations

Now that we have substituted the input into the function, we need to perform the necessary calculations to find the value of g(25)g(25). We can start by evaluating the expression inside the parentheses.

g(25) = 24(-14)

Step 3: Multiply the Numbers

Next, we need to multiply 24 by -14 to find the final value of g(25)g(25).

g(25) = -336

Conclusion

In this article, we have seen how to find the value of a function for a given input. We used the function g(x)=24(x−39)g(x) = 24(x - 39) as an example and found the value of g(25)g(25) by substituting the input into the function and performing the necessary calculations. The final value of g(25)g(25) is -336.

Discussion

Now that we have found the value of g(25)g(25), let's discuss the different options that were given in the problem.

Option A: 561

This option is incorrect because the value of g(25)g(25) is not 561.

Option B: 311

This option is also incorrect because the value of g(25)g(25) is not 311.

Option C: -18

This option is incorrect because the value of g(25)g(25) is not -18.

Option D: 336

This option is incorrect because the value of g(25)g(25) is not 336.

Final Answer

The final answer is -336.

Frequently Asked Questions

Q: What is the value of g(25)g(25)?

A: The value of g(25)g(25) is -336.

Q: How do I find the value of a function for a given input?

A: To find the value of a function for a given input, you need to substitute the input into the function and perform the necessary calculations.

Q: What is the difference between a linear function and a non-linear function?

A: A linear function has a constant rate of change, while a non-linear function does not have a constant rate of change.

Q: How do I evaluate an expression inside parentheses?

A: To evaluate an expression inside parentheses, you need to follow the order of operations (PEMDAS).

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

References

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Introduction

In our previous article, we explored how to find the value of a function for a given input. In this article, we will delve deeper into the world of function evaluation and answer some of the most frequently asked questions.

Q&A Session

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, on the other hand, is a statement that two expressions are equal.

Q: How do I determine if a relation is a function?

A: To determine if a relation is a function, you need to check if each input corresponds to only one output. If an input corresponds to more than one output, then the relation is not a function.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible input values for which the function is defined.

Q: What is the range of a function?

A: The range of a function is the set of all possible output values that the function can produce.

Q: How do I evaluate a function with multiple variables?

A: To evaluate a function with multiple variables, you need to substitute the values of each variable into the function and perform the necessary calculations.

Q: What is the difference between a linear function and a non-linear function?

A: A linear function has a constant rate of change, while a non-linear function does not have a constant rate of change.

Q: How do I graph a function?

A: To graph a function, you need to plot the points on a coordinate plane that satisfy the function's equation.

Q: What is the difference between a function and a relation?

A: A function is a relation that assigns each input to exactly one output, while a relation is a set of ordered pairs that may or may not be a function.

Q: How do I find the inverse of a function?

A: To find the inverse of a function, you need to swap the x and y values of the function's equation and solve for y.

Q: What is the difference between a one-to-one function and a many-to-one function?

A: A one-to-one function assigns each input to exactly one output, while a many-to-one function assigns multiple inputs to the same output.

Q: How do I determine if a function is one-to-one?

A: To determine if a function is one-to-one, you need to check if each output corresponds to only one input.

Q: What is the difference between a function and a mapping?

A: A function is a relation that assigns each input to exactly one output, while a mapping is a relation that assigns each input to one or more outputs.

Q: How do I find the composition of two functions?

A: To find the composition of two functions, you need to substitute the output of the first function into the input of the second function.

Q: What is the difference between a function and a relation in terms of the number of inputs and outputs?

A: A function has exactly one output for each input, while a relation may have multiple outputs for each input.

Conclusion

In this article, we have answered some of the most frequently asked questions about function evaluation. We have covered topics such as the difference between a function and an equation, the domain and range of a function, and how to evaluate a function with multiple variables.

Frequently Asked Questions

Q: What is the difference between a function and a relation?

A: A function is a relation that assigns each input to exactly one output, while a relation is a set of ordered pairs that may or may not be a function.

Q: How do I determine if a relation is a function?

A: To determine if a relation is a function, you need to check if each input corresponds to only one output.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible input values for which the function is defined.

Q: What is the range of a function?

A: The range of a function is the set of all possible output values that the function can produce.

Q: How do I evaluate a function with multiple variables?

A: To evaluate a function with multiple variables, you need to substitute the values of each variable into the function and perform the necessary calculations.

References