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Which of the following functions from $Z$ into $Z$ are bijections? |
$f(x) = x^3$ $f(x) = x + 2$ $f(x) = 2x + 1$ $f(x) = x^2 + 1$ |
$f(x) = x + 2$ |
The correct answer is Option (2) → $f(x) = x + 2$ ## Here, $f(x) = x + 2 \Rightarrow f(x_1) = f(x_2)$ $x_1 + 2 = x_2 + 2 \Rightarrow x_1 = x_2$ Let $y = x + 2$ $x = y - 2 \in Z, \forall y \in Z$ Hence, $f(x)$ is one-one and onto. |
