Question

find the domain of the function defined by FX=sin^-1(x-1).
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Answer 1

Answer:

We know that sin-1 x is defined for x ∈ [-1,1]

∴ f(x) = sin-1 √(x-1) is defined if

⇒ 0 ≤ √(x-1)≤ 1

⇒ 0 ≤ x - 1 ≤ 1 [∵√(x-1 ≥ 0 and -1 ≤ √(x-1 ≤ 1]

⇒ 1 ≤ x ≤ 2

∴ x ∈ [1,2]