If $f(x) = 3x + 2$ And $g(x) = X^2 - X$, Find The Value Of \$f(1) - 1$[/tex\].

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Introduction

In this article, we will explore the concept of algebraic expressions and how to solve them. We will use the given functions $f(x) = 3x + 2$ and $g(x) = x^2 - x$ to find the value of $f(1) - 1$. This problem requires us to apply the concept of function evaluation and basic algebraic operations.

Understanding the Functions

Before we proceed, let's understand the given functions.

Function f(x)

The function $f(x) = 3x + 2$ is a linear function, which means it has a constant rate of change. The coefficient of x is 3, and the constant term is 2.

Function g(x)

The function $g(x) = x^2 - x$ is a quadratic function, which means it has a variable rate of change. The coefficient of x^2 is 1, and the coefficient of x is -1.

Evaluating f(1)

To evaluate $f(1)$, we need to substitute x = 1 into the function $f(x) = 3x + 2$.

def f(x):
    return 3*x + 2

result = f(1)
print(result)

When we run this code, we get the result:

result = 5

Therefore, $f(1) = 5$.

Finding f(1) - 1

Now that we have found $f(1) = 5$, we can proceed to find $f(1) - 1$.

result = f(1) - 1
print(result)

When we run this code, we get the result:

result = 4

Therefore, $f(1) - 1 = 4$.

Conclusion

In this article, we have solved a simple algebraic expression using the given functions $f(x) = 3x + 2$ and $g(x) = x^2 - x$. We have evaluated $f(1)$ and then found $f(1) - 1$. The result is $f(1) - 1 = 4$.

Final Answer

The final answer is 4\boxed{4}.

Additional Resources

For more information on algebraic expressions and functions, please refer to the following resources:

  • Khan Academy: Algebra
  • MIT OpenCourseWare: Algebra
  • Wolfram MathWorld: Algebra

Related Problems

If you want to practice more problems like this, please try the following:

  • Find the value of $g(2)$.
  • Evaluate $f(x)$ at x = -1.
  • Find the value of $f(2) - 2$.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using mathematical symbols.

Q: What is a function?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). It is a way to describe a relationship between variables using mathematical symbols.

Q: How do I evaluate a function?

A: To evaluate a function, you need to substitute the input value into the function and perform the necessary mathematical operations. For example, if we have the function $f(x) = 3x + 2$ and we want to evaluate it at x = 1, we would substitute x = 1 into the function and get $f(1) = 3(1) + 2 = 5$.

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

A: A function is a relation between a set of inputs and a set of possible outputs, while an algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. A function can be thought of as a special type of algebraic expression that has a specific output for each input.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and perform the necessary mathematical operations. For example, if we have the expression $2x + 3x + 4$, we can combine the like terms $2x$ and $3x$ to get $5x + 4$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which mathematical operations to perform first when evaluating an algebraic expression. The order of operations is:

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

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. You can use a graphing calculator or software to help you graph the function.

Q: What is the domain and range of a function?

A: The domain of a function is the set of all possible input values, while the range is the set of all possible output values. For example, if we have the function $f(x) = 1/x$, the domain is all real numbers except 0, and the range is all real numbers except 0.

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 and solve for y. For example, if we have the function $f(x) = 2x + 1$, the inverse function is $f^{-1}(x) = (x - 1)/2$.

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

A: A linear function is a function that has a constant rate of change, while a quadratic function is a function that has a variable rate of change. A linear function can be represented by the equation $f(x) = mx + b$, while a quadratic function can be represented by the equation $f(x) = ax^2 + bx + c$.

Q: How do I solve a system of equations?

A: To solve a system of equations, you need to find the values of the variables that satisfy all the equations. You can use substitution or elimination methods to solve the system of equations.

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

A: A function is a relation between a set of inputs and a set of possible outputs, while a relation is a set of ordered pairs that satisfy a certain condition. A function can be thought of as a special type of relation that has a specific output for each input.

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A: To determine if a function is one-to-one or many-to-one, you need to check if the function passes the horizontal line test. If the function passes the horizontal line test, it is one-to-one. If it does not pass the horizontal line test, it is many-to-one.

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A: A function can have only one output for each input, while a relation can have multiple outputs for each input.

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A: To find the domain and range of a function in terms of the number of outputs, you need to count the number of outputs for each input. The domain is the set of all possible input values, while the range is the set of all possible output values.

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A: A function can have only one input for each output, while a relation can have multiple inputs for each output.

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A: To find the domain and range of a function in terms of the number of inputs, you need to count the number of inputs for each output. The domain is the set of all possible input values, while the range is the set of all possible output values.

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

A: A function can have only one ordered pair for each input, while a relation can have multiple ordered pairs for each input.

Q: How do I find the domain and range of a function in terms of the number of ordered pairs?

A: To find the domain and range of a function in terms of the number of ordered pairs, you need to count the number of ordered pairs for each input. The domain is the set of all possible input values, while the range is the set of all possible output values.

Q: What is the difference between a function and a relation in terms of the number of x-coordinates?

A: A function can have only one x-coordinate for each output, while a relation can have multiple x-coordinates for each output.

Q: How do I find the domain and range of a function in terms of the number of x-coordinates?

A: To find the domain and range of a function in terms of the number of x-coordinates, you need to count the number of x-coordinates for each output. The domain is the set of all possible input values, while the range is the set of all possible output values.

Q: What is the difference between a function and a relation in terms of the number of y-coordinates?

A: A function can have only one y-coordinate for each input, while a relation can have multiple y-coordinates for each input.

Q: How do I find the domain and range of a function in terms of the number of y-coordinates?

A: To find the domain and range of a function in terms of the number of y-coordinates, you need to count the number of y-coordinates for each input. The domain is the set of all possible input values, while the range is the set of all possible output values.

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

A: A function can have only one point for each input, while a relation can have multiple points for each input.

Q: How do I find the domain and range of a function in terms of the number of points?

A: To find the domain and range of a function in terms of the number of points, you need to count the number of points for each input. The domain is the set of all possible input values, while the range is the set of all possible output values.

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

A: A function can have only one line for each input, while a relation can have multiple lines for each input.

Q: How do I find the domain and range of a function in terms of the number of lines?

A: To find the domain and range of a function in terms of the number of lines, you need to count the number of lines for each input. The domain is the set of all possible input values, while the range is the set of all possible output values.

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

A: A function can have only one curve for each input, while a relation can have multiple curves for each input.

Q: How do I find the domain and range of a function in terms of the number of curves?

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