What are the steps in addition on function?

Adding Functions: A Simple Guide (Because Math Doesn’t Have to Be Scary!)

Remember when you first learned to add regular numbers? Well, guess what? You can add functions too! It’s true! Just like you can combine 2 and 3 to get 5, you can smoosh two functions together to create a brand new one. This “smooshing” is what mathematicians call “operations on functions,” and today, we’re tackling addition.

So, how does this function-adding magic work? Let’s break it down.

Decoding the Math Lingo

First things first, let’s get the notation out of the way. If you’ve got two functions, let’s call them f(x) and g(x) (because why not?), then their sum is written as (f + g)(x). Don’t let that scare you! All it really means is that for any number you plug in for x, you add the result of f(x) to the result of g(x). Think of it like this:

(f + g)(x) = f(x) + g(x)

Basically, you’re just adding the two functions together. Simple as that!

The Super-Easy Steps for Adding Functions

Alright, ready to get your hands dirty? Here’s the lowdown on adding functions:

1. Meet Your Functions: First, you gotta know who you’re working with. Let’s say we have f(x) = x² + 3x – 4 and g(x) = 2x + 3. These are our players.

2. Write It Out: Now, write down the addition problem using our fancy notation: (f + g)(x) = f(x) + g(x). Then, swap in the actual functions:

(f + g)(x) = (x² + 3x – 4) + (2x + 3)

3. Tidy Up! This is where the fun begins! Combine all the like terms to make the expression look nice and clean. Remember combining like terms from algebra? It’s coming back to haunt you! In our case:

(f + g)(x) = x² + (3x + 2x) + (-4 + 3)


(f + g)(x) = x² + 5x – 1

Voila! We’ve added the functions!

4. Mind the Domain! Okay, this is a little bit tricky, but stick with me. The “domain” of a function is basically all the possible x values you can plug in without breaking the math. When you add functions, the domain of the new function (f+g)(x) is where the domains of the original functions, f(x) and g(x), overlap.

• Polynomial Power: If both f(x) and g(x) are polynomials (stuff like x² + 3x – 4), then their domains are all real numbers. That means the domain of (f + g)(x) is also all real numbers. Easy peasy!
• Rational Reality Check: If you’ve got fractions with x on the bottom (rational functions), you need to watch out for values of x that would make the denominator zero. Those values are not allowed in the domain.
• Radical Restrictions: Square roots (or other even roots) are picky. You can’t take the square root of a negative number (at least, not without getting into imaginary numbers!), so you need to make sure the stuff inside the square root is always zero or positive.

Domain Example Time!

Let’s say f(x) = √(x + 2) and g(x) = 1/(x – 3).

• The domain of f(x) is x ≥ -2 (because we need x + 2 to be zero or positive).
• The domain of g(x) is all real numbers except x = 3 (because we can’t divide by zero).

So, the domain of (f + g)(x) is x ≥ -2 AND x ≠ 3. In other words, it’s all the numbers from -2 up to infinity, but we have to skip over 3.

Putting It to Work: Evaluating Added Functions

Once you’ve got your combined function (f + g)(x), you can actually use it! Plug in a number for x, and you’ll get a result. It’s like magic!

Example Time Again!

Remember our functions f(x) = x² + 3x – 4 and g(x) = 2x + 3, which gave us (f + g)(x) = x² + 5x – 1?

Let’s find (f + g)(2). Just swap x for 2:

(f + g)(2) = (2)² + 5(2) – 1 = 4 + 10 – 1 = 13

So, (f + g)(2) = 13. Ta-da!

The “Do It In Pieces” Method

Here’s a cool trick: you can also find the value by plugging into f(x) and g(x) separately and then adding the results.

Using the same example, to find (f + g)(2):

• f(2) = (2)² + 3(2) – 4 = 4 + 6 – 4 = 6
• g(2) = 2(2) + 3 = 4 + 3 = 7
• f(2) + g(2) = 6 + 7 = 13

Same answer! It’s just a different way to get there.

Final Thoughts

Adding functions might seem a little weird at first, but it’s really just about combining things you already know. Follow these steps, and you’ll be adding functions like a pro in no time! And who knows? Maybe you’ll even start seeing functions everywhere you go. Okay, maybe not everywhere, but you’ll definitely have a new tool in your math belt.