what-is-range-of-a-function-f-x-x-1-x-2-1-

Question Number 95140 by i jagooll last updated on 23/May/20

what is range of a function

f (x) = \frac{x + 1}{\sqrt{x^{2} - 1}}

Commented by bobhans last updated on 23/May/20

\sqrt{x^{2} - 1} is valid when x^{2} > 1 . so we have domain

as (\min_{f}, 1) \cup (1, \inf) . in first interval

the function goes from - 1 to 0, since

limit (f, x, \min_{f}) = - 1 and the second

interval the function goes from \inf down

to 1, since limit (f, x, 1, + \infty) = \inf and

limit (f, x, \inf) = 1 . so the range is

(- 1, 0) \cup (1, \infty)

Commented by i jagooll last updated on 23/May/20

thank you