Question

Find the domain of the following functions:

`tan^-1 (sqrt(9 - x^2))`

Answer 1

f(x) = `tan^-1 (sqrt(9 - x^2))`

We know the domain of `tan^-1x` is `(- oo, oo)` and range is `(- pi/2, pi/2)`

So, the domain of f(x) = `tan^-1 (sqrt(9 - x^2))` is the set of values of x satisfying the inequality

`- oo ≤ sqrt(9 - x^2) ≤ oo`

⇒ 9 – x² ≥ 0

⇒ x² ≤ 9

⇒ |x| ≤ 3

Since tan x is an odd function and symmetric about the origin, tan^–1 x should be an increasing function in its domain.

∴ Domain is `(2"n" + 1)^(pi/2)`