Which of the following functions cannot have | vedclass

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(D) function $f: A 	o B$ is invertible if and only if it is a bijection (both one-to-one and onto).Option $A$: $y = e^x$ is a strictly increasing fun

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$f : R 	o R^+ ; y = e^{[x]}$

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(D) function $f: A 	o B$ is invertible if and only if it is a bijection (both one-to-one and onto).Option $A$: $y = e^x$ is a strictly increasing function from $R$ to $R^+$,hence it is a bijection and invertible.Option $B$: $y = \log|x|$ for $x \in R^+$,$y = \log x$,which is a strictly increasing function from $R^+$ to $R$,hence it is a bijection and invertible.Option $C$: $y = \sin^3x$ is a strictly increasing function on $\left[ - \frac{\pi}{2}, \frac{\pi}{2} ight]$ mapping to $[-1, 1]$,hence it is a bijection and invertible.Option $D$: $y = e^{[x]}$ where $[x]$ is the greatest integer function. For any $x \in [0, 1)$,$[x] = 0$,so $y = e^0 = 1$. Since the function takes the same value for all $x$ in the interval $[0, 1)$,it is not one-to-one (many-to-one). Therefore,it is not a bijection and its inverse cannot be defined.

Which of the following functions cannot have their inverse defined? (where $[.] \to$ greatest integer function)

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