Can anyone explain me the logic behind this?

[timber axle]

So if the graph meets at one point,then the intersection between the two set have null elements or not?

[upbeat yarrow]

well, what is a point in $\bR^{2}$? Both of these sets appear to be subsets of $\bR^{2}$

[frozen birch]

Moosey

[upbeat yarrow]

Does what I said make sense?

@timber axle

[pulsar galleon]

It is just asking for you to find solutions (x,y) to y=e^x and y=e^(-x)

This implies e^x = e^(-x)
which implies x= -x
which implies x = 0
So all the points in the intersection have point x= 0 , y = e^0=1

(0,1)

[timber axle]

If the intersection of two function is 0,1 then what is the value of A intersection B?

[timber axle]

No

[upbeat yarrow]

is (0,1) a set in R^2?

[noble token]

"value" is not the word you're looking for. The intersection is a set with one element.

[timber axle]

Yes

[timber axle]

K and what would be that? (0,1)?

[noble token]

Yes

[timber axle]

Then what would be the answer?

[dapper prawn]

for the 31st oneis the answer b?

@timber axle for the 9th one well if u simplify it then ull get e^x=x

so is it c?

[timber axle]

I understand the answer would be 0,1 but how do we reach from there to answer b?

[pulsar galleon]

You only intersect sets. You don’t intersect functions. That doesn’t make sense.

Perhaps I can go over what an intersection is.

You can intersect 2 sets. You could intersect more than 2 sets and it would still make sense.

So if A and B are two arbitrary sets, then we define the intersection of A and B to be the set of elements are are in A and B.

Now I will also define a function so you don’t get that mixed up either.

Functions are “defined” on a domain.

For example, arctan is defined for all real numbers, but squareroot is defined for all non-negative numbers.

We call all the places that a function that is defined on the domain of the function.

Notice that the domain is a set.

Then once you have established what the domain for the function is, it needs to have an output for each input in the domain.

So if x is in the domain and you input it into the function, then f(x) is the output for that input.

It is important to understand that functions can only have 1 output for every input.

Like in the squareroot function:
squareroot(4) = 2. It does not equal -2 because the squareroot function can only have 1 output per input.

There is also an image of a function. It is the set of possible outputs. So you would input everything in the domain into the function and anything that could be outputted is in the image of the function.

Notice that the image of a function is a set.

There is also a codomain/range.

You can also input subsets S of the domain into the function and get the image f(S) which would be all possible outputs if the inputs are all in S.

Hopefully that clears that up.

[timber axle]

yeah

[timber axle]

my answer key says A

[upbeat yarrow]

is $R$ the set of real numbers?

[frozen birch]

Moosey

[upbeat yarrow]

I assumed so, but if answer key says it's A, maybe it's not