Calculate F(5) For F(x) = 8x - 3: Step-by-Step Solution

Hey everyone! Today, we're diving into a fun little math problem. We've got a function, f(x) = 8x - 3, and our mission is to figure out what f(5) is. Sounds like a piece of cake, right? Let's break it down step by step and make sure we understand exactly what's going on. This isn't just about getting the right answer; it's about understanding the process so we can tackle similar problems with confidence. So, grab your thinking caps, and let's get started!

Understanding Functions

Before we jump into the calculation, let's take a moment to really understand what a function is. Think of a function like a machine. You feed it an input (in this case, our x), and it spits out an output (our f(x)). The function has a specific rule that it follows to transform the input into the output. In our case, the rule is 8x - 3. This means whatever number we put in for x, we multiply it by 8 and then subtract 3. So, when we're asked to find f(5), we're essentially asking: "What happens when we feed 5 into this machine?" This concept of functions is super important in mathematics, and it pops up everywhere, from simple equations to complex calculus problems. Getting a solid grasp on this now will definitely pay off later. We use functions to model real-world relationships, predict outcomes, and solve all sorts of problems. They're a fundamental tool in the mathematician's toolbox. Now that we've refreshed our understanding of functions, let's get back to our specific problem and see how this knowledge helps us solve it.

Plugging in the Value

Okay, so we know that f(x) = 8x - 3, and we want to find f(5). This means we need to replace every x in the equation with the number 5. It's like we're substituting x with its value. So, let's do it! We replace x with 5, and we get f(5) = 8(5) - 3. See how simple that is? We've just taken the abstract x and made it concrete by plugging in the specific value we're interested in. This is a crucial step because it transforms our function from a general rule into a specific calculation. Now, all that's left is to do the arithmetic. We've got multiplication and subtraction to deal with, and we need to make sure we follow the correct order of operations (PEMDAS/BODMAS, anyone?). This is where the rubber meets the road – we take our understanding of the function and turn it into a numerical answer. It's like translating a sentence from one language to another; we're taking the function notation and translating it into a numerical result. And once we have that result, we'll have successfully answered the question: What is f(5)?

Performing the Calculation

Now comes the fun part – the actual calculation! Remember our equation: f(5) = 8(5) - 3. According to the order of operations (PEMDAS/BODMAS), we need to do the multiplication before the subtraction. So, let's multiply 8 by 5. What do we get? 8 times 5 is 40. Great! Now our equation looks like this: f(5) = 40 - 3. We're almost there! We've simplified the expression down to a single subtraction. This is where basic arithmetic skills come into play. We're taking away 3 from 40. Can you picture it? Imagine having 40 of something and then removing 3. How many are left? That's right, it's 37! So, f(5) = 37. We've done it! We've successfully calculated the value of the function at x = 5. This step-by-step calculation is what transforms the abstract function into a concrete answer. It's the bridge between the symbolic world of algebra and the numerical world of arithmetic. And now, with our answer in hand, we can confidently move on to the next step: checking our answer against the given options.

Checking the Answer

We've calculated that f(5) = 37. Awesome! But before we declare victory, let's just double-check our answer against the options provided. This is a really important step in problem-solving, not just in math but in life in general. It's about making sure we haven't made any silly mistakes and that our answer makes sense in the context of the problem. So, let's look at the options: A. 40, B. 43, C. 37, D. 45. Do you see our answer there? Yes! Option C is 37. This confirms that our calculation is correct. We multiplied 8 by 5 to get 40, then subtracted 3 to get 37. It all checks out! This feeling of confirmation is so satisfying, isn't it? It's the moment when all our hard work pays off and we can confidently say, "We got it!" Checking our answer is also a great way to reinforce our understanding of the problem. It forces us to revisit our steps and make sure everything is logical and consistent. So, always remember to take that extra minute to check your work – it can save you from making avoidable errors.

The Correct Answer

Alright, drumroll please… The correct answer is C. 37! We did it! We successfully calculated f(5) for the function f(x) = 8x - 3. Give yourselves a pat on the back – you've earned it! This wasn't just about getting the right answer; it was about understanding the process, breaking down the problem, and applying our knowledge of functions and order of operations. Remember, math isn't just about memorizing formulas; it's about understanding concepts and developing problem-solving skills. And you've demonstrated those skills beautifully in this exercise. So, what have we learned today? We've learned how to evaluate a function at a specific point, how to apply the order of operations, and how to check our answers to ensure accuracy. These are valuable skills that will serve you well in future math problems and beyond. So, keep practicing, keep exploring, and keep challenging yourselves. The world of mathematics is full of fascinating puzzles just waiting to be solved!

Final Thoughts and Tips for Success

So, there you have it! We've successfully navigated this little math problem and arrived at the correct answer. But more importantly, we've reinforced some key concepts about functions and how they work. Remember, the key to tackling these types of problems is to break them down into smaller, manageable steps. Don't try to do everything at once! Start by understanding what the question is asking, then identify the relevant information and tools you need to solve it. In this case, we needed to understand the function notation and the order of operations. Once you have a clear plan, the calculation itself becomes much easier. Another tip for success is to practice regularly. The more you work with functions and equations, the more comfortable you'll become with them. It's like learning a new language – the more you use it, the more fluent you become. And finally, don't be afraid to ask for help if you're stuck. Math can be challenging, and there's no shame in seeking guidance from a teacher, tutor, or friend. Collaboration is a powerful tool for learning and problem-solving. So, keep up the great work, and remember to enjoy the process of learning! Math can be a fascinating and rewarding subject, and with a little practice and persistence, you can conquer any challenge that comes your way.

I hope this explanation has been helpful and insightful. Feel free to revisit this example whenever you need a refresher on how to evaluate functions. And remember, the world of mathematics is full of exciting discoveries just waiting to be made. Keep exploring, keep learning, and keep having fun with math!