which of the following is true about the function below? 1/√x+10

A. Its domain is (-∞,0]and its range is (0,∞)

B. Its domain is (-10,∞) and its range is (0,∞)

C. Its domain is (-10, ∞) and its range is (-∞,∞) D. Its domain is[-10,∞) and its range is

(-∞,0) U (0,∞)

... ?

The true answer is

D. Its domain is (-10,∞) and its range is

(-∞,0) U (0,∞)

proof

f (x) = 1/√x+10, so domain can be found on solving x+10>0, it is (-10,∞)

the inverse of f is g (x) = 1/x² - 10, domain of g is the range of f, so domain of g is x²# 0 implies domain of g is (-∞,0) U (0,∞) (all real apart from 0)

so the range of f is (-∞,0) U (0,∞)