If f -1(x) is the inverse of f(x), which statements must be true? check all that apply. a. the range of f -1(x) is the range of f(x). b. f -1(f(x)) = x c. the range of f -1(x) is the domain of f(x). d. f(f -1(x)) = x e. the domain of f -1(x) is the range of f(x). f. the domain of f -1(x) is the domain of f(x).

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).