how do u approach a question like that?
write an equation that satisfy the following simultaneously
a) the domain of f is (-Infinity, 0) U (0,infinity)
b) f is continuous on its domain (that is everywhere except at x = 0)
c) lim f(x) as x--> 1- (from the left) = - infinti
d) lim f(x) as x --> 1+ (from the right) = 0
e) f(1) = 2.
The Attempt at a Solution
i know from the domain that x cant be zero
so the equation is probably going to a fraction, let say (x+1)/x.
(x+1)/x domain is (-Infinity, 0) U (0,infinity) and its continuous on its domain.
f(1) = (1+1)/1 = 2/1 = 2.
so a, b, and e are correct
but c and d, i dont know how to do them.