Find a function with the following characteristics:
D {xer|x=/=4}
R {yer|y=/=9}
f(x) increasing over entire domain
Impossible?
D: x≠4
R: y≠9
f increasing
You know that the logistic function is always increasing, so start with
y = 9/(1+e^-x)
That is defined for all x, and 0<y<9. To exclude x=4, just make a hole there:
y = 9(x-4) / (x-4)(1+e^-x)