Inverse of y=|x|???????

Question

does y=|x| have an inverse that works for all values of x? Explain please.

Answer 1

well if the modulus function causes negative and positive values to become positive the inverse function cause positive values top become both positive and negative. The inverse function is:

y = (+ or -) x where x > (or equal to) 0

the condition on x is needed as in the original function only positive outcomes are posible so only positive values can be inputted to the inverse function

Answer 2

No.

The domain of y = | x | is all real numbers.  The range is only non-negative numbers.

The inverse would be:

y = ±x (for x ≥ 0)

The domain is only non-negative numbers and the range becomes all real numbers.  (They swap).

Also, the inverse is not a function, since each value of x results in two values of y.