Mastering Algebra Functions: A Student's Guide to Problem-Solving

Algebra can feel like a maze, right? You’re not alone if you've stared at equations wondering, “What’s next?” Understanding how to navigate functions is key, especially when tackling problems like the one involving ( F(x) = x^2 + 5x ) and ( G(x) = 2x + 1 ). So let’s break it down together!

Imagine you're on a treasure hunt. Each function is a map that leads you closer to the treasure—well, in this case, the answer to the problem! Today, we’ll find out what ( F(5) ) and ( G(6) ) yield when we plug in the numbers. It’s kind of like baking, isn’t it? You follow a recipe (or in our case, a function) and mix your ingredients together step by step.

First up, let’s take a peek at ( F(x) = x^2 + 5x ). When we substitute ( x = 5 ) into this function, we’re interacting with a quadratic equation—think of it as a roller coaster ride that gets steep in a hurry.

So, here’s the first step—we substitute:

[ F(5) = 5^2 + 5(5) ] You know what? That feels a bit like following the bouncing ball, doesn’t it? We get:

[ = 25 + 25 ] [ = 50 ]

Alright, we’ve got our first treasure: ( F(5) = 50 )! Now, it’s time to move on and unearth the next piece of treasure with ( G(x) = 2x + 1 ). Let’s see what the function gives us with ( x = 6 ):

[ G(6) = 2(6) + 1 ] Calculating that, we follow another path:

[ = 12 + 1 ] [ = 13 ]

Now we have ( G(6) = 13 ). So, what’s left? Well, it's like putting the final piece in a jigsaw puzzle. We just need to add ( F(5) ) and ( G(6) ) together:

[ F(5) + G(6) = 50 + 13 ] [ = 63 ]

And there you have it—the grand total! The treasure chest reveals ( 63 ) as the answer to our problem. Transforming numbers and expressions into an answer is much like delving into a narrative where each mathematical function tells a part of the story. You see, algebra isn’t just about numbers; it’s about understanding relationships.

Whether you're gearing up for an exam or simply brushing up on your skills, having a solid grasp of functions like these will empower you. You’ll not only conquer exam questions that pop up but also develop a keen sense of how to approach various algebraic challenges.

In summary, getting the hang of functions in algebra means you'll be a step ahead in your studies. So take these insights, practice with confidence, and let your skills shine as you tackle whatever comes your way!