If $f(x)=2x^2+1$, What Is $f(x)$ When $ X = 3 X=3 X = 3 [/tex]?A. 1 B. 7 C. 13 D. 19
Understanding the Function
The given function is $f(x)=2x^2+1$. This is a quadratic function, where the variable x is squared and then multiplied by 2, and finally, 1 is added to the result. To find the value of f(x) when x = 3, we need to substitute x = 3 into the function.
Substituting x = 3 into the Function
To find the value of f(x) when x = 3, we substitute x = 3 into the function $f(x)=2x^2+1$. This gives us:
Simplifying the Expression
Now, we simplify the expression by evaluating the exponent and then multiplying the result by 2. The exponent (3)^2 is equal to 9. Therefore, the expression becomes:
Multiplying 2 and 9
Next, we multiply 2 and 9, which gives us 18. Therefore, the expression becomes:
Adding 18 and 1
Finally, we add 18 and 1, which gives us 19. Therefore, the value of f(x) when x = 3 is 19.
Conclusion
In conclusion, when x = 3, the value of f(x) is 19. This is the correct answer.
Answer Options
The answer options are:
A. 1 B. 7 C. 13 D. 19
Choosing the Correct Answer
Based on our calculation, the correct answer is D. 19.
Why is this Important?
Understanding how to solve for f(x) when x = 3 is important because it demonstrates the ability to apply mathematical functions to real-world problems. In many fields, such as science, engineering, and economics, mathematical functions are used to model and analyze complex systems. Therefore, being able to solve for f(x) when x = 3 is a fundamental skill that can be applied in a variety of contexts.
Real-World Applications
The concept of solving for f(x) when x = 3 has many real-world applications. For example, in physics, the equation for the motion of an object under the influence of gravity is a quadratic function. In economics, the equation for the demand for a product is also a quadratic function. Therefore, being able to solve for f(x) when x = 3 is an important skill that can be applied in a variety of real-world contexts.
Tips and Tricks
Here are some tips and tricks for solving for f(x) when x = 3:
- Make sure to substitute x = 3 into the function correctly.
- Simplify the expression by evaluating the exponent and then multiplying the result by 2.
- Multiply 2 and 9 carefully.
- Add 18 and 1 carefully.
- Check your answer to make sure it is correct.
Common Mistakes
Here are some common mistakes to avoid when solving for f(x) when x = 3:
- Not substituting x = 3 into the function correctly.
- Not simplifying the expression correctly.
- Not multiplying 2 and 9 carefully.
- Not adding 18 and 1 carefully.
- Not checking the answer to make sure it is correct.
Conclusion
In conclusion, solving for f(x) when x = 3 is an important skill that can be applied in a variety of real-world contexts. By following the steps outlined in this article, you can ensure that you are solving for f(x) when x = 3 correctly. Remember to substitute x = 3 into the function correctly, simplify the expression, multiply 2 and 9 carefully, add 18 and 1 carefully, and check your answer to make sure it is correct.
Q: What is the function f(x) when x = 3?
A: The function f(x) when x = 3 is 19. This is calculated by substituting x = 3 into the function f(x) = 2x^2 + 1 and simplifying the expression.
Q: How do I substitute x = 3 into the function f(x) = 2x^2 + 1?
A: To substitute x = 3 into the function f(x) = 2x^2 + 1, you simply replace x with 3. This gives you f(3) = 2(3)^2 + 1.
Q: What is the value of (3)^2?
A: The value of (3)^2 is 9. This is calculated by multiplying 3 by itself.
Q: How do I simplify the expression f(3) = 2(9) + 1?
A: To simplify the expression f(3) = 2(9) + 1, you multiply 2 and 9, which gives you 18. Then, you add 1 to 18, which gives you 19.
Q: Why is it important to simplify the expression f(3) = 2(9) + 1?
A: It is important to simplify the expression f(3) = 2(9) + 1 because it helps you to get the correct answer. If you do not simplify the expression, you may get an incorrect answer.
Q: What are some common mistakes to avoid when solving for f(x) when x = 3?
A: Some common mistakes to avoid when solving for f(x) when x = 3 include:
- Not substituting x = 3 into the function correctly
- Not simplifying the expression correctly
- Not multiplying 2 and 9 carefully
- Not adding 18 and 1 carefully
- Not checking the answer to make sure it is correct
Q: How can I check my answer to make sure it is correct?
A: You can check your answer by plugging x = 3 back into the original function f(x) = 2x^2 + 1 and simplifying the expression. If you get the same answer, then your answer is correct.
Q: What are some real-world applications of solving for f(x) when x = 3?
A: Some real-world applications of solving for f(x) when x = 3 include:
- Physics: The equation for the motion of an object under the influence of gravity is a quadratic function.
- Economics: The equation for the demand for a product is also a quadratic function.
- Engineering: The equation for the stress on a beam is a quadratic function.
Q: Why is it important to understand how to solve for f(x) when x = 3?
A: It is important to understand how to solve for f(x) when x = 3 because it demonstrates the ability to apply mathematical functions to real-world problems. In many fields, such as science, engineering, and economics, mathematical functions are used to model and analyze complex systems.
Q: How can I practice solving for f(x) when x = 3?
A: You can practice solving for f(x) when x = 3 by working through example problems and checking your answers to make sure they are correct. You can also try solving for f(x) when x = different values to see how the answer changes.
Q: What are some tips for solving for f(x) when x = 3?
A: Some tips for solving for f(x) when x = 3 include:
- Make sure to substitute x = 3 into the function correctly
- Simplify the expression carefully
- Multiply 2 and 9 carefully
- Add 18 and 1 carefully
- Check your answer to make sure it is correct