What Is $f(x)$ When $x=3$?A. $ F ( 3 ) = 0 F(3)=0 F ( 3 ) = 0 [/tex] B. $f(3)=5$ C. $f(3)=3$ D. $ F ( 3 ) = 2 F(3)=2 F ( 3 ) = 2 [/tex]

Mar 9, 2025 by ADMIN 147 views

**What is $f(x)$ when $x=3$?**

Understanding the Problem

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). The function is often denoted by a symbol, such as $f(x)$, where $x$ is the input and $f(x)$ is the output. To find the value of $f(x)$ when $x=3$, we need to understand the function and its behavior.

Function Notation

Function notation is a way of writing a function as a mathematical expression. It consists of a symbol, such as $f$, followed by the input variable, $x$, in parentheses. For example, $f(x)$ represents a function that takes $x$ as input and produces an output.

Evaluating a Function

To evaluate a function, we need to substitute the input value into the function expression. In this case, we want to find $f(3)$, which means we need to substitute $x=3$ into the function expression.

Example Function

Let's consider a simple example function: $f(x) = 2x + 1$. This function takes an input $x$ and produces an output that is twice the input plus one.

Evaluating $f(3)$

To find $f(3)$, we substitute $x=3$ into the function expression:

f(3) = 2(3) + 1

Using the order of operations, we first multiply $2$ and $3$:

f(3) = 6 + 1

Then, we add $6$ and $1$:

f(3) = 7

Therefore, $f(3) = 7$.

Conclusion

In conclusion, to find $f(x)$ when $x=3$, we need to understand the function and its behavior. We can evaluate a function by substituting the input value into the function expression. In this example, we used the function $f(x) = 2x + 1$ and found that $f(3) = 7$.

Answer

The correct answer is:

B. $f(3)=7$

Note: The other options are incorrect because they do not match the result of evaluating the function $f(x) = 2x + 1$ when $x=3$.

Additional Examples

Here are a few more examples of evaluating functions:

Example 1: $f(x) = x^2 + 2x + 1$, find $f(4)$.
- $f(4) = (4)^2 + 2(4) + 1$
- $f(4) = 16 + 8 + 1$
- $f(4) = 25$
Example 2: $f(x) = 3x - 2$, find $f(5)$.
- $f(5) = 3(5) - 2$
- $f(5) = 15 - 2$
- $f(5) = 13$

Tips and Tricks

When evaluating functions, make sure to follow the order of operations (PEMDAS):

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.

Q: What is a function in mathematics?

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 often denoted by a symbol, such as $f(x)$, where $x$ is the input and $f(x)$ is the output.

Q: How do I evaluate a function?

A: To evaluate a function, you need to substitute the input value into the function expression. For example, if you have the function $f(x) = 2x + 1$ and you want to find $f(3)$, you would substitute $x=3$ into the function expression:

f(3) = 2(3) + 1

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

A: The order of operations 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.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and eliminate any unnecessary operations. For example, if you have the expression $2x + 3x + 1$, you can combine the like terms $2x$ and $3x$ to get $5x + 1$.

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

A: A function is a relation between a set of inputs and a set of possible outputs, while an equation is a statement that says two expressions are equal. For example, $f(x) = 2x + 1$ is a function, while $2x + 1 = 5$ is an equation.

Q: How do I graph a function?

A: To graph a function, you need to plot the points on a coordinate plane and connect them with a smooth curve. 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 you have the function $f(x) = 1/x$, the domain is all real numbers except zero, and the range is all real numbers except zero.

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 you have the function $f(x) = 2x + 1$, the inverse 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 of the form $f(x) = mx + b$, where $m$ and $b$ are constants. A quadratic function is a function of the form $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

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

A: To find the zeros of a function, you need to set the function equal to zero and solve for x. For example, if you have the function $f(x) = 2x + 1$, you can set it equal to zero and solve for x:

2x + 1 = 0

2x = -1

x = -1/2

Therefore, the zero of the function is $x = -1/2$.

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. For example, $f(x) = 2x + 1$ is a function, while ${(1, 3), (2, 5), (3, 7)}$ is a relation.

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 one function into the input of the other function. For example, if you have the functions $f(x) = 2x + 1$ and $g(x) = x^2 + 1$, you can find the composition $f(g(x))$ by substituting $g(x)$ into $f(x)$:

f(g(x)) = f(x^2 + 1)

f(g(x)) = 2(x^2 + 1) + 1

f(g(x)) = 2x^2 + 3

Therefore, the composition of the two functions is $f(g(x)) = 2x^2 + 3$.

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

A: A function is a relation between a set of inputs and a set of possible outputs, while a graph is a visual representation of the function. For example, $f(x) = 2x + 1$ is a function, while the graph of the function is a visual representation of the function on a coordinate plane.

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

A: To find the derivative of a function, you need to use the power rule, the product rule, and the quotient rule. For example, if you have the function $f(x) = 2x^2 + 3x + 1$, you can find the derivative using the power rule:

f'(x) = 4x + 3

Therefore, the derivative of the function is $f'(x) = 4x + 3$.

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

A: A function is a relation between a set of inputs and a set of possible outputs, while a sequence is a list of numbers in a specific order. For example, $f(x) = 2x + 1$ is a function, while the sequence ${1, 3, 5, 7, 9}$ is a sequence.

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

A: To find the sum of a function, you need to add the function to itself. For example, if you have the function $f(x) = 2x + 1$, you can find the sum by adding the function to itself:

f(x) + f(x) = 2x + 1 + 2x + 1

f(x) + f(x) = 4x + 2

Therefore, the sum of the function is $f(x) + f(x) = 4x + 2$.