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  4. Let f: R arrow R be function defined by f(x) = sin (2x -3), then f is

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Q. Let f : R $\rightarrow$ R be function defined by f(x) = sin (2x -3), then f is

Relations and Functions - Part 2

Solution:

Since sin (2x - 3) is a periodic function with period $\pi$, therefore f is not injective. Also, f is not surjective as its range [-1, 1] is a proper subset of its co-domain R.