Help writing an equation that satisfies some statements

[ammsa]

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 can't 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 don't know how to do them.
any help?

 

[tiny-tim]

welcome to pf!

hi ammsa! welcome to pf!

(have an infinity: ∞ )

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.

no, the question must be wrong …

"b) f is continuous on its domain (that is everywhere except at x = 0)" is inconsistent with c) d) and e) …

those three conditions clearly make the function discontinuous at x = 1