Hey guys! Let's dive into a super straightforward math problem today. We're given a function f(x) = 5x + 40, and our mission, should we choose to accept it, is to find out what f(x) equals when x is 5. Sounds simple? That's because it is! No need to break out the calculus textbooks or summon your inner mathematician. This is a basic substitution problem that anyone can tackle with a little bit of focus. So, let's get started and break down each step so you can totally nail it.

Understanding the Function

Before we jump into plugging in numbers, let's make sure we understand what the function f(x) = 5x + 40 is telling us. In simple terms, this function takes an input value (which we call x), multiplies it by 5, and then adds 40 to the result. The function f(x) is essentially a recipe: you give it an x, it follows the steps, and spits out a new value. For example, if we put in x = 2, the function would do 5 * 2 + 40, which equals 50. So, f(2) = 50. Understanding this basic concept is crucial before we move forward. Think of functions as little machines that transform numbers based on a specific rule. In this case, the rule is "multiply by 5 and then add 40." This sets the stage for solving our problem, making it easier to grasp what we're actually doing when we substitute x with 5. Always remember, functions are your friends in math; they just want to take your input and give you a modified output! Now that we're all comfy with what a function does, let's get to the fun part: plugging in the numbers and solving for f(5).

Substituting x with 5

Okay, now comes the easy part. We're asked to find the value of f(x) when x = 5. This means we need to substitute every instance of x in the function f(x) = 5x + 40 with the number 5. So, we replace x with 5, and our equation becomes f(5) = 5 * 5 + 40. See? We just swapped out the x for a 5. Now it’s just a matter of doing the arithmetic to find out what f(5) actually equals. This is where the order of operations comes into play (remember PEMDAS or BODMAS?). We need to do the multiplication before we do the addition. So, first, we calculate 5 * 5, which equals 25. Now our equation looks like this: f(5) = 25 + 40. We're almost there! Just one more simple addition problem to solve. This substitution step is super important. Make sure you replace every instance of x with the given value. Sometimes, functions can be more complex and have x in multiple places, so always double-check! Alright, let’s wrap this up and get our final answer.

Calculating the Result

Alright, we're in the home stretch! We've already substituted x with 5, and we've simplified our equation to f(5) = 25 + 40. Now, all that's left to do is add 25 and 40 together. If you add 25 and 40, you get 65. So, f(5) = 65. And that's it! We've found our answer. When x is 5, the value of the function f(x) = 5x + 40 is 65. Wasn't that easy? Sometimes, math problems seem intimidating, but when you break them down into smaller, manageable steps, they become much simpler to solve. This is a great example of how substitution works in functions. You take the given value, plug it in, and then follow the order of operations to get your result. Remember, practice makes perfect! The more you work with functions and substitution, the more comfortable you'll become with them. So, next time you see a function problem, don't sweat it. Just remember the steps we went through, and you'll be able to tackle it like a pro!

Final Answer

So, after all that, the final answer is:

f(5) = 65

That's all there is to it! You now know how to evaluate a simple function at a given point. Remember, the key is to understand what the function is doing, substitute correctly, and then follow the order of operations. You've got this!

Practice Problems

Want to test your newfound skills? Here are a few practice problems similar to the one we just solved. Try them out, and you can check your answers with the solutions provided below.

1. If g(x) = 3x + 10, what is g(4)?
2. If h(x) = 7x - 5, what is h(2)?
3. If k(x) = 2x + 15, what is k(5)?

Solutions

1. g(4) = 3 * 4 + 10 = 12 + 10 = 22
2. h(2) = 7 * 2 - 5 = 14 - 5 = 9
3. k(5) = 2 * 5 + 15 = 10 + 15 = 25

How did you do? Hopefully, you nailed all of them! If not, don't worry; just go back and review the steps we covered earlier. Remember, practice is key to mastering these types of problems.

Real-World Applications

You might be wondering, "Okay, this is cool, but where would I ever use this in real life?" Well, functions are used everywhere! Here are a few examples:

• Calculating Costs: Imagine you're ordering pizzas for a party. The pizza place charges $10 per pizza plus a $5 delivery fee. You could represent the total cost as a function of the number of pizzas you order: c(p) = 10p + 5, where c(p) is the total cost and p is the number of pizzas. If you want to know how much it would cost to order 3 pizzas, you'd calculate c(3) = 10 * 3 + 5 = $35.
• Converting Temperatures: You can convert temperatures from Celsius to Fahrenheit using a function: F(C) = (9/5)C + 32, where F(C) is the temperature in Fahrenheit and C is the temperature in Celsius. If you want to know what 25 degrees Celsius is in Fahrenheit, you'd calculate F(25) = (9/5) * 25 + 32 = 77 degrees Fahrenheit.
• Tracking Distance: Suppose you're driving at a constant speed of 60 miles per hour. You can represent the distance you've traveled as a function of time: d(t) = 60t, where d(t) is the distance in miles and t is the time in hours. If you want to know how far you'll travel in 2 hours, you'd calculate d(2) = 60 * 2 = 120 miles.

These are just a few examples, but functions are used in countless other fields, including science, engineering, economics, and computer science. Understanding functions is a fundamental skill that will help you in many different areas of life.

Conclusion

And there you have it! We've successfully solved the problem of finding f(5) when f(x) = 5x + 40. We walked through the steps of understanding the function, substituting x with 5, calculating the result, and even explored some real-world applications of functions. Remember, math doesn't have to be scary. By breaking down problems into smaller steps and practicing regularly, you can build your skills and confidence. So, keep practicing, keep exploring, and most importantly, keep having fun with math! You're now equipped to tackle similar problems with ease. Go forth and conquer those functions!