Question

Give a formula for a function whose domain is all negative values of x except x=-5

Answer 1

Somthing like this ?

f(x)= 1/(x+5) + 1/(1 - x/|x|)

Answer 2

Does it make sense ?

Answer 3

how did you come up with it?

Answer 4

well it has two parts.

This part is undefined when x=-5 (you get a division by 0):
1/(x+5)

This part is undefined for non-negative numbers:
1/(1 - x/|x|)

notice that |x| means absolute value of x, so:
x/|x| will be 1 for postive values of x, -1 for negative values of x and undefined for x=0

only for negative numbers we wont have a division by zero below:
1/(1 - x/|x|)

Let me know if this is clear :)

Answer 5

this is clear. but there are no simpler equations to use?

Answer 6

f(x)= 1/(x+5) + log( -x )

Answer 7

f(x) = log(-x) / (x+5)