What is the result of adding f and g in set addition?

[thomasrules]

Let f = {(-4.4),(-2,4),(1,3),(3,5),(4,6)}

and g = {(-4,2),(-2,1),(0,2),(1,2),(2,2),(4,4)}

Determine a)f + g

 

[chroot]

What are your thoughts?

- Warren

 

[thomasrules]

honestly I'm confused...
f(x)=-4x+4? etc...?
It's not (-4,4)+(-4,2)

 

[chroot]

What's the value of the function f at, say, -4?

What's the value of the function g with the same input, -4?

What's the sum of the values of the two functions, given the same input, -4?

- Warren

 

[thomasrules]

wouldn't it be (-8,6)

 

[chroot]

No, the input -- the value on the left -- is still -4. The summed outputs of both functions, however, is indeed 4+2 = 6.

You have thus found the first input-output pair of the sum of f+g, (-4, 6).

In english, this means if you plug -4 into f(x) + g(x), you get f(-4) + g(-4) = 4+2 = 6.

- Warren

 

[daveb]

Is this adding two sets f and g or is this adding function f to function g? The way it's written I assumed it was creating a union of two sets.

 

[thomasrules]

but what's the equation of f(x)=?
It looks like you set x to zero

why does left side -4 stay the same ...?

 

[chroot]

daveb,

You have a good point. This question is a little ambiguous. However, simply taking the union of two sets means that the resulting function f+g is multivalued at -4, for example, which means it's no longer a function.

Adding the outputs of the two functions is also a little tricky, since f is defined at 3, for example, while g is not. The sum of the two functions at 3 is thus also undefined, since anything + undefined = undefined.

The first set is f(x), for x values -4, -2, 1, 3, and 4.

The second set is g(x), for x values -4, -2, 0, 1, 2, and 4.

The only input values common to both functions are -4, -2, 1, and 4. These are thus the input values acceptable to the function f+g. All other possible input values have no defined output.

The output values of f+g are each the sum of the outputs of f and g at the same point. Thus, if you plug in -4 to f+g, you get f(-4) + g(-4) = 4+2 = 6.

- Warren

 

[thomasrules]

oh so ur saying that when adding them you have to have the same x value

 

[chroot]

Yes. When you give the function f the input -4, it produces the output 4. When you give the function g the input -4, it produces the output 2.

When you give the sum of the two functions, f+g, the input -4, the result is the sum of the outputs, 4+2 = 6.

Thus, one member of the resulting set for f+g should be (-4, 6).

- Warren

 

[thomasrules]

thank you my friend