Question
Download Solution PDFThe domain of sin-1 5x is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- The domain of a function f(x) is the set of values of x for which the function is defined.
- The value of sin θ always lies in the interval [-1, 1].
- sin-1 (sin θ) = θ.
- sin (sin-1 x) = x.
Calculation:
Let's say that sin-1 5x = θ
⇒ sin (sin-1 5x) = sin θ
⇒ sin θ = 5x
Since, -1 ≤ sin θ ≤ 1
⇒ -1 ≤ 5x ≤ 1
⇒
⇒ x ∈
∴ The domain of the function is the closed interval
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