Question
Download Solution PDFFind the domain of sin-1 3x
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
| Function | Domain | Range of Principal Value |
| sin-1 x | [-1, 1] | [-π/2, π/2] |
| cos-1 x | [-1, 1] | [0, π] |
| csc-1 x | R - (-1, 1) | [-π/2, π/2] - {0} |
| sec-1 x | R - (-1, 1) | [0, π] - {π/2} |
| tan-1 x | R | (-π/2, π/2) |
| cot-1 x | R | (0, π) |
Calculation:
Let f(x) = sin-1 3x
As we know domain of sin-1 x is x ∈ [-1, 1]
So, -1 ≤ 3x ≤ 1
\(\Rightarrow \rm \frac{-1}{3} \leq x \leq \frac{1}{3}\)
Hence domain of sin-1 3x is \(\left[\frac{-1}{3} , \frac{1}{3} \right ]\)
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