Which one of the following is a bijective fun | vedclass

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(A) function $f: \mathbb{R} 	o \mathbb{R}$ is bijective if it is both one-one (injective) and onto (surjective).$1$. For $f(x) = |x|$,$f(1) = 1$ and

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$2x - 5$

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(A) function $f: \mathbb{R} 	o \mathbb{R}$ is bijective if it is both one-one (injective) and onto (surjective).$1$. For $f(x) = |x|$,$f(1) = 1$ and $f(-1) = 1$. Since $f(1) = f(-1)$ but $1 
eq -1$,it is not one-one.$2$. For $f(x) = x^2$,$f(1) = 1$ and $f(-1) = 1$. Since $f(1) = f(-1)$ but $1 
eq -1$,it is not one-one.$3$. For $f(x) = x^2 + 1$,$f(1) = 2$ and $f(-1) = 2$. Since $f(1) = f(-1)$ but $1 
eq -1$,it is not one-one.$4$. For $f(x) = 2x - 5$:- One-one: Let $f(x) = f(y)$. Then $2x - 5 = 2y - 5$,which implies $2x = 2y$,so $x = y$. Thus,it is one-one.- Onto: Let $y = 2x - 5$. Then $x = \frac{y + 5}{2}$. For every $y \in \mathbb{R}$,there exists $x = \frac{y + 5}{2} \in \mathbb{R}$ such that $f(x) = y$. Thus,it is onto.Since $f(x) = 2x - 5$ is both one-one and onto,it is a bijective function.

Which one of the following is a bijective function on the set of real numbers?

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