/sci/ - Science & Math

[Anonymous No.5043187]

for what f(x) and g(x) does f(x)/g(x)=f(x)?

f(x) /neq 0
g(x) /neq 1

[Anonymous No.5043191]

>>5043187
stupid tex

[Carl No.5043212]

What range and domain?

[Anonymous No.5043265]

>>5043212
All reals.

[Anonymous No.5043274]

>>5043265
None?

Since f(x) is never 0 you can say f(x)/g(x)*(1/f(x) = f(x) * (1/f(x))

Which means 1/g(x) = 1

Unless we're working with the extended reals?

[Anonymous No.5043283]

Aslong as f(x) and g(x) are unequal to 0, g(x) has to be 1 and if f(x) is zero, then u can pick any g(x). g(x) equal to zero makes no sense.

[Anonymous No.5043342]

inb4 f(x) = inf and g(x) = 0

[Carl No.5043366]

>>5043342
I was about to post it.

[Anonymous No.5043385]

f(x) = e^x
g(x) = x^0*lim h->0 [h/(e^h - 1)] = 1/c =/= 0 and defined
f(x)/g(x) = e^x/1/c = ce^x = e^x lim h->0 [(e^h - 1)/h] = lim h->0 (e^(x+h) - e^x)/h = e^x.

[Anonymous No.5043397]

f(x) /neq 0
g(x) /neq 1

This could mean not the functions 0 and 1.

In that case, choose functions where g(x) = 1 where f(x) /= 0.

f(x) = 1 for x /= 0 and f(0) = 0
g(x) = 1 for x /= 0 and g(0) = 2

[Anonymous No.5043419]

You could rephrase this as
>When does 1 \neq 1

[Anonymous No.5043463]

>>5043385
Guess my answer wasn't correct enough.