Prove or disprove ? f(A/B)=f(A)/f(B)
1 Answer
Jun 12, 2017
This identity is generally false...
Explanation:
In general this will be false.
A simple example would be:
f(x) = 2
Then:
f(1/1) = 2 != 1 = 2/2 = f(1)/f(1)
Bonus
For what kind of functions
Note that:
f(1) = f(1/1) = f(1)/f(1) = 1
f(0) = f(0/x) = f(0)/f(x)" " for anyx
So either
If
f(x) = x^n
Then:
f(a/b) = (a/b)^n = a^n/b^n = f(a)/f(b)
There are other possibilities for
f(x) = abs(x)^c" " for any real constantc
f(x) = "sgn"(x)*abs(x)^c" " for any real constantc