The SBAF activation function is as follows - Note : 0<=x<=1 $$ f(x) = \frac{1}{1+ kx^a(1-x)^{1-a}} $$ Where k and a are constants. I know we have to show that integral $\int_{-\infty}^{\infty} f(x)\, dx$ is not equal to 1. But I'm not able to integrate this. Can someone help me out ?

  • $\begingroup$ Well, the first problem is that the function gets negative values. That already rules out the possibility of it being a PDF. $\endgroup$ – Matti P. Apr 15 at 6:57
  • $\begingroup$ I'm sorry , I forgot to mention 0<=x<=1. $\endgroup$ – Hari Charan Apr 15 at 7:05
  • $\begingroup$ Also k and a are positive constants. $\endgroup$ – Hari Charan Apr 15 at 7:06

$0\leq f(x) \leq 1$ for all $x \in (0,1)$. So $\int_0^{1}f(x)dx \leq 1$ and equality can hold only of $f(x)=1$ for all $x$. But $f(x) \neq 1$ for any $x \in (0,1)$!.


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