Which of the following functions is invertibl | vedclass

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(A) function $f: A 	o B$ is invertible if and only if it is a bijection,meaning it is both one-one (injective) and onto (surjective).$1$. For $f(x) =

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$f(x) = 2^x$

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(A) function $f: A 	o B$ is invertible if and only if it is a bijection,meaning it is both one-one (injective) and onto (surjective).$1$. For $f(x) = 2^x$,if we consider the domain as $\mathbb{R}$ and codomain as $(0, \infty)$,the function is strictly increasing (one-one) and covers all positive real values (onto). Thus,it is invertible.$2$. For $f(x) = x^3 - x$,the derivative $f'(x) = 3x^2 - 1$ changes sign at $x = \pm \frac{1}{\sqrt{3}}$,so it is not monotonic and not one-one on $\mathbb{R}$.$3$. For $f(x) = x^2$,$f(1) = f(-1) = 1$,so it is not one-one.Therefore,$f(x) = 2^x$ is the correct answer.

Which of the following functions is invertible?

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