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## Homework Statement

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.

any help?