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# Worked example: Evaluating functions from equation

Learn how to evaluate f(x)=49-x² at x=5. Created by Sal Khan.

## Want to join the conversation?

• Can anybody help me find the output, k, when the input, t, is −7.
k = 10t-19
k = ?

I need a hand. Thank you
• You just neet to replace "t" with the given value "-7"
k = 10(-7)-19
Then, follow order of operations rules to calculate the value of "k".
Give it a try. Comment back if you get stuck or have questions.
• 1. Can a function have name like add(x) instead of f(x)?
2. Can a function have more than 1 argument, like f(a, b, c)?
3. Can a function's argument have a name like "apes", "apples" instead of "x", "y"?
• 1. Yes. In mathematics it is more common to use a single letter (sometimes a Greek letter), but a function name can be anything. After all it's just a way to communicate to other humans what you're talking about, changing a name doesn't change the math.
2. Yes. A simple example is f(x,y) = x * y.
3. Yes. See answer 1: single letter names are conventional, but not required. They're all just names. You could even draw pictures instead of using letters - in fact, Khan Academy does that in some early math videos.
• What are the general rules for solving functions?
• like terms should ALWAYS be combined, that's one thing you can keep in mind
• Can Someone Help Me Solve This Function?
f(0)^2
where f(x)=3x+4
• Find f(0): f(0) = 3(0) + 4
Once you know, f(0), square the result.
• does anyone know how to do this?
• how to do what
• How do you know where the output is?
• To get the output (or know where it is) you have to solve the equation for y (y is the output). So to graph it you'll use the input as the x coordinate and the output as the y coordinate.
• why not just put the number there instead of using functions?
• Nice question. There's nothing wrong with doing that, of course!
However, with function notation, specifying the input (`x`) value is much easier.
As you know, `y = 4x + 2` and `f(x) = 4x + 2` are the same. `y` and `f(x)` are interchangeable.

To show how they're both evaluated at `x = 3`:
- `x = 3: y = 4(3) + 2 = 14`
- `f(3) = 4(3) + 2 = 14`

Instead of specifying that `x = 3` then writing the substituted `y` equation, you can just say `f(3)`, which implies that `x = 3` (as the `3` is in place of `x`) and plugged into the function.

In this way, among others, function notation is advantageous compared to the `y=` notation! It makes the working out much clearer, and thinking of things as a function can really help with certain math problems later on.

Happy learning.
• So the "f" in f(x) stands for function? As in solve the function with whatever the x variable may be?