Question

If f(x1)+f(x2)=f(x1+x2) for all real numbers x1 and x2, which of the following could define f?
A) f(x)=x+1
B)f(x)=2x
C)f(x)=1/x
D)f(x)=e^x
E)f(x)=x^2

I have no idea how to go about this, if someone can explain it to me.

Answer 1

given f(x), if you want to find f(x1),
replace all 'x' in f(x) by 'x1'
for example, if f(x) = x^3 - x
f(x1) = (x1)^3 - x1
got this ?

Answer 2

No I do not.

Answer 3

which part, u have doubt with ?

Answer 4

The whole thing itself. The wording is confusing.

Answer 5

what you have to do is to find, for each option
(1) f(x1)+f(x2)
(2) f(x1+x2)
and check, for which option are these two equal.

Answer 6

if, x1 , x2 confuses you, you can find
(1) f(a)+f(b)
(2) f(a+b)
where f(a) is found by replacing 'x' in f(x) by a.
f(b) is found by replacing 'x' in f(x) by b.
and check whether they come out to be equal.

Answer 7

Let me do option A) for you, you check for others.
f(x1) = x1+1
f(x2) = x2+1
f(x1+x2) = x1+x2+1
but f(x1)+f(x2) = x1+1 +x2+1 = x1 + x2+2
which does not equal f(x1+x2).
so, option A is not correct.
try others.

Answer 8

I get it now. Thanks!

Answer 9

which option you got ?

Answer 10

I ended up with E.

Answer 11

well, E is incorrect.
f(x1) = x1^2
f(x2) = x2^2
f(x1+x2) = (x1+x2)^2 = x1^2+2x1*x2 + x2^2
but f(x1)+f(x2) = x1^2+x2^2 only
which does not equal f(x1+x2).
so, option E
is not correct.

Answer 12

did u try B) ??

Answer 13

Yes. I ended up with D.

Answer 14

even, thats incorrect....try B)

Answer 15

were you just guessing ?
show your work with option B)

Answer 16

I was not guessing. Like I said, I have no idea what I'm doing.

Answer 17

i gave you an idea with that explanation..why don't you follow that for option B)