Prove that the Greatest integer Function f : R R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Function f : R R, given by f(x) = [x] ;1 x 2, f(x) = 1 f(1) = 1 and f(1.1) = 1 f is not one-one. f takes only integer values, therefore range(f) = set of integers,which is not equal to R, codomain. Therefore, f is not onto.

Prove that the Greatest integer Function f : R R, given by f(x) =…

If $\cos\Big(\sin^{-1}\frac{2}{5}+\cos^{-1}\text{x}\Big)=0$ find the value of X.

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