FunctionHard
Question
Range of f(x) = log√5 (√2(sin x - cos x) + 3) is
Options
A.[0, 1]
B.[0, 2]
C.
D. none of these
Solution
f(x) = log√5 (√2 (sin x - cos x) + 3) is
we know that
- √2 ≤ sin x - cos x ≤ √2, ∀ x ∈ R [since -
≤ a sin x + b cos x ≤ 
]
⇒ - 2 ≤ √2 (sin x - cos x) ≤ 2
⇒ 1 ≤ √2 (sin x - cos x) + 3 ≤ 5
⇒ 0 ≤ log√5 (√2(sin x - cos x) + 3) ≤ 2
Hence range is [0, 2]
we know that
- √2 ≤ sin x - cos x ≤ √2, ∀ x ∈ R [since -
≤ a sin x + b cos x ≤ ]⇒ - 2 ≤ √2 (sin x - cos x) ≤ 2
⇒ 1 ≤ √2 (sin x - cos x) + 3 ≤ 5
⇒ 0 ≤ log√5 (√2(sin x - cos x) + 3) ≤ 2
Hence range is [0, 2]
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