Q. 205.0( 1 Vote )
Mark the correct A. bijection
B. injection but not a surjection
C. surjection but not an injection
D. neither an injection nor a surjection
Given that f : [–1/2, 1/2] → [π/2, π/2] where f(x) = sin–1 (3x – 4x3)
Put x = sinθ in f(x) = sin–1 (3x – 4x3)
⇒ f(x=sinθ) = sin–1 (3sinθ – 4sinθ3)
⇒ f(x) = sin–1 (sin3θ)
⇒ f(x) = 3θ
⇒ f(x) = 3 sin–1x
If f(x) = f(y)
3 sin–1x = 3 sin–1y
⇒ x = y
So, f is one-one.
y = 3 sin–1x
∵ x ϵ R also y ϵ R so f is onto.
Hence, f is bijection.
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