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1. If \( A=\left\{0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}\right\} \) and \( f: A \rightarrow B \) is a surjection defined by \( f(x)=\cos x \), then find \( B \). |
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Answer» \(f: A \to B\) is a surjection and defined by \(f(x) = cos x\) Then \(f(A) = B\) But \(A = \left\{0, \frac\pi6, \frac\pi4,\frac\pi3,\frac\pi2\right\}\) \(\therefore f(A) = \left\{cos 0, cos\frac\pi6, cos\frac\pi4, cos\frac\pi3, cos\frac\pi2\right\}\) \(= \left\{1, \frac{\sqrt3}{2}, \frac1{\sqrt2}, \frac12, 1\right\}\) \(\therefore B = \left\{1,\frac{\sqrt3}2, \frac1{\sqrt2},\frac12, 1\right\}\) |
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