Question

The largest interval lying in `((-π)/2, π/2)` for which the function, f(x) = `4^(-x^2) + cos^-1(x/2 - 1) + log(cosx)`, is defined, is ______.

Options

• `[-π/4, π/2)`

• `[0, π/2)`

• [0, π]

• `(-π/2, π/2)`

Answer 1

The largest interval lying in `((-π)/2, π/2)` for which the function, f(x) = `4^(-x^2) + cos^-1(x/2 - 1) + log(cosx)`, is defined, is `underlinebb([0, π/2)`.

Explanation:

Given that

f(x) = `4^(-x^2) + cos^-1(x/2 - 1) + log(cosx)`

f(x) is defined if `-1 ≤ (x/2 - 1) ≤ 1` and cos x > 0

⇒ `0 ≤ x/2 ≤ 2` and `-π/2 < x < π/2`

⇒ 0 ≤ x ≤ 4 and `-π/2 < x < π/2`

∴ `x ∈ [0, π/2)`