Solving For F(x) When X = 10: A Step-by-Step Guide

Hey everyone! Today, we're diving into a super simple math problem that's all about functions and evaluating them. Don't worry, it's not as scary as it sounds! We're going to break down how to solve for f(x) when x equals 10, using the equation f(x) = x/2 + 8. This is a fundamental concept in algebra, so understanding it is key. This guide will walk you through the process step-by-step, making sure you grasp every detail. Let's get started, shall we?

Understanding the Basics of Functions

Before we jump into the problem, let's quickly review what a function is. In math, a function is like a machine. You put something in (an input), and the machine does something to it (a process), and then spits out something else (an output). In our case, the input is x, the process is dividing x by 2 and adding 8, and the output is f(x). We denote a function as f(x), where f is the name of the function, and x is the variable or the input. This notation tells us that the value of the function depends on the value of x. Pretty neat, huh?

So, when we say f(x) = x/2 + 8, we're saying that whatever value x has, we need to divide it by 2 and then add 8 to find the value of the function f(x). This is also called evaluating the function for a given x. Remember, understanding this concept is crucial, and it will serve as a building block for more complex problems later on. We'll be doing a lot of substitution, so let's prepare to plug in the value for x and keep it moving!

This simple concept underpins a huge amount of mathematics. Functions are used everywhere, from calculating the trajectory of a ball to predicting the stock market. Therefore, the simple exercise we will undertake here is far more important than it may initially appear. Functions are the cornerstone of algebra and calculus, so mastering them will open doors to a deeper understanding of higher-level math concepts. Also, being able to manipulate these equations is crucial for problem-solving in various fields, so keep this in mind. With practice, these types of problems will become second nature, and you'll be well on your way to mathematical mastery. Ready to solve for our problem? Keep reading!

Step-by-Step Solution

Alright, let's get down to business and solve for f(x) when x = 10. The equation we're working with is f(x) = x/2 + 8. We need to find the value of the function when x is 10. Here's how to do it, step-by-step:

1. Substitute the value of x: The first step is to replace every instance of x in the equation with the value 10. This gives us f(10) = 10/2 + 8.
2. Perform the division: Next, we need to divide 10 by 2. 10 divided by 2 is 5. So now our equation looks like this: f(10) = 5 + 8.
3. Perform the addition: Finally, we add 5 and 8 together. 5 + 8 equals 13. Therefore, f(10) = 13.

So, the answer is 13. This is pretty straightforward, right? We simply replaced x with its given value and followed the order of operations to solve for f(x). Now, we'll go through it in more detail. Each step should be clear, and you can always revisit it for a better understanding. Don't worry if it takes a bit of time to grasp the whole thing. Practicing more examples will help to reinforce the concept and make you more confident in your approach. Keep going!

In essence, what we've done is find the output of the function f when the input is 10. Functions are versatile tools, and being able to evaluate them is a core skill in mathematics and other fields. You'll encounter functions in various contexts, from science to engineering. This simple example has given you a solid foundation for evaluating more complex functions in the future. Remember the steps: substitute the value of x, perform any necessary calculations according to the order of operations, and then you've got your answer. This method will become your best friend in algebra and beyond. You've got this!

The Correct Answer and Explanation

Okay, so we've calculated that f(10) = 13. Looking back at the multiple-choice options, we can see that option C is the correct answer. The other options (A. 4, B. 9, D. 36) are incorrect because they don't follow the correct steps to evaluate the function. To make sure you've truly understood the concept, let's quickly review the process.

We started with the function f(x) = x/2 + 8 and the given value x = 10. We substituted 10 for x, which gave us f(10) = 10/2 + 8. Then, we followed the order of operations. First, we performed the division (10/2 = 5), and then we performed the addition (5 + 8 = 13). Therefore, the correct answer is indeed 13. This is a very common type of question, so knowing how to solve it can help you do well on tests and understand future concepts. Congratulations, you've successfully evaluated a function! You did great! Keep practicing, and you'll be able to solve these problems with ease.

The ability to correctly solve the problem shows you understand not only the concept of a function but also how to substitute values and perform basic arithmetic operations. The more problems you solve, the more confident you will become. Keep practicing and keep up the great work. Remember, mathematics is all about practice. The more you practice, the better you get. You are already on the right track!

Conclusion: You Got This!

So, there you have it, guys! We've successfully found the value of f(x) when x = 10. The answer is 13, which means the correct option is C. This problem highlights the fundamentals of functions, substitution, and basic arithmetic. Remember that the process is more important than just getting the right answer. Making sure you understand each step will help you with more complicated functions. Functions might seem a little daunting at first, but with a bit of practice, you will become a pro. Keep practicing, and you will build a solid foundation. You're doing great! Keep up the hard work, and you will see how the world of mathematics opens up to you.

This simple exercise is a gateway to more complex mathematical ideas. From here, you can explore other types of functions, such as quadratic and exponential functions. With each step you take, you are building your math skills and your confidence. Don't get discouraged if you encounter a problem that seems tough; that's part of the learning process. The key is to break the problem into smaller parts, understand the concepts, and keep trying. That's the best way to master any subject, and it goes for any kind of problem. So keep going, keep practicing, and keep learning. Well done, everyone! You got this!