Answer: Hello there!
we have the function f(x) = IxI/x
Then this function can be piecewise writen as:
f(x) = 1 if x > 0
f(x) = -1 if x < 0
because:
suposse that n is a number greater than 0, then:
f(n) = InI/n = n/n = 1
and this is independent of the number n, so for all the positive values of x, we have f(x) = 1
and
f(-n) = I-nI/(-n) = n/(-n) = -1
and again, this does not depend on the value of n, so for all the negative values of x, we have f(x) = -1.
On the other hand, the Heaviside function is defined as:
H(x) = 1 if x>0
H(x) = 0 if x<0
Then the difference is that, when the Heaviside function takes the value of 0 for negative values of x, our function f(x) takes the value of -1 for negative values of x.
