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

Answer :

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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