alleryThe DOMAIN of y = tan x is:
A{x ∈ ℝ : -1 ≤ x ≤ 1}
BAll real numbers
C{x ∈ ℝ : x ≠ (2n+1)π/2, n ∈ ℤ}
D{x ∈ ℝ : x ≠ nπ, n ∈ ℤ}
Answer & Solution
Correct answer: C. {x ∈ ℝ : x ≠ (2n+1)π/2, n ∈ ℤ}
tan x = sin x / cos x is undefined where cos x = 0, i.e. at x = (2n+1)π/2. Hence domain = ℝ \ {(2n+1)π/2 : n ∈ ℤ}.
Range of tan x is all of ℝ.
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