Question

Find the range of the function f(x) = log₂(log_1/2(x² + 4x + 4))

Answer 1

Let g(x) = (x² + 4x + 4) = (x + 2)²

Thus D_g = R & R_g = [0, ∞)

So, – ∞ < log_1/2(x² + 4x + 4) < ∞

⇒ 0 < log_1/2(x² + 4x + 4) < ∞

⇒ – ∞ < log₂(log_1/2(x² + 4x + 4)) < ∞

Thus, R_f = (–∞, ∞)