Question

Find the largest possible domain of the real valued function f(x) = `sqrt(4 - x^2)/sqrt(x^2 - 9)`

Answer 1

f(x) = `sqrt(4 - x^2)/sqrt(x^2 - 9)`

Here `sqrt(4 - x^2) > 0` 4 – x2 > 0 ∴ x2 > 4 x < 2 and x > – 2

Here `sqrt(x^2 - 9) > 0` x2 – 9 > 0 ∴ x2 > 9 x > 3 and x < – 3

∴ No largest possible domain

The domain is null set