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What does f(x,y) mean?

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Jadav Payeng


( 5 months ago )

I know from the chapter "functions" that f(x)f(x) is a function of xx and to roughly put it, it maps xx values to another set called co-domain where all the yy values are.

But I also sometimes see f(x,y)f(x,y) on internet. I can guess that it means some expression in xx and yy.

I'm not familiar with them yet and they aren't in my high school syllabus but I'd love to know more about and I have a few questions,

  • What type of function is this? What's it called?

  • What does is represent? Can you also represent f(x,y)f(x,y) using arrow diagram between 22 sets?

  • Is (x,y)(x,y) in f(x,y)f(x,y) an ordered pair? Or f(x,y)f(x,y) is same as writing f(y,x)

Pooja Bhardwaj


( 5 months ago )

You can call f(x,y)f(x,y) might be called a function of two variables. An example that might be helpful would be something like f(x,y)=x2+y2f(x,y)=x2+y2. This function takes in two numbers, takes their squares and adds them. Note that a function of two variables doesn't need to do the same thing to both variables. We could also make a function g(x,y)=x3+xy+1g(x,y)=x3+xy+1 for example. You can represent them using an arrow diagram. Your set to the left of your arrow will be the set of ordered pairs of (x,y)(x,y). And yes, the you do need to think of (x,y)(x,y) as an ordered pair. It is not necessarily the case that f(x,y)=f(y,x)f(x,y)=f(y,x). See the g(x,y)g(x,y) example above and note that g(0,1)=1g(0,1)=1 but g(1,0)=2g(1,0)=2.

Many functions in real life are functions of more than one variable. An example from physics: the gravitational pull an object experiences from a planet is a function of both the planet's mass and the distance to the planet.

what's your interest