Monday, 16 August 2021

Let f(x)=sin⁡x+αx,x∈R, where α is a fixed real number. Prove the function f is one-to-one if and only if α≥1 or α≤−1.
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Define f:R→R by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...