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

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

amistre64 · Answer

thats part of the definition of a linear function

amistre64 · Answer

of course, lower math classes like to muddy affine functions with linears.  an affine function is a linear, plus a nonzero constant

anonymous · Answer

Hi, sorry could you go into more detail, I'm still not catching on. I don't think i've ever heard of affine functions?

amistre64 · Answer

have you heard of a linear function?

amistre64 · Answer

and if you look at the options, youll notice that one of them has a constant add to it .... which might correlate with something ive posted

amistre64 · Answer

otherwise, you can try out the rule that they defined for it ...

f(x+y) = f(x) + f(y)

anonymous · Answer

D right? E is the constant?

amistre64 · Answer

um, no.  nothing is being added in that option.  and "e" is a number like "pi"

amistre64 · Answer

$$e^{x+y}=e^x~e^y$$therefore that doent follow the rule defined

anonymous · Answer

Oh I get it now 2 is the constant, that means that B is the answer right?

amistre64 · Answer

B is the answer :)

B is the function of a line that passes thru the origin (its a linear function)

the affine function is A,  its a linear function (+1)

anonymous · Answer

Thanks so much!! :)