Question
Which of the following functions from $Z$ into $Z$ are bijections?
- (a) $f(x) = {x^3}$
- (b) $f(x) = x + 2$ ✓ Correct
- (c) $f(x) = 2x + 1$
- (d) $f(x) = {x^2} + 1$
Relations and Functions — Class 12 Maths Solution
Step-by-step Solution
Here $f(x) = x + 2 \Rightarrow f\left( {{x_1}} \right) = f\left( {{x_2}} \right)$
${x_1} + 2 = {x_2} + 2 \Rightarrow {x_1} = {x_2}$
Let $y = x + 2$
$x = y - 2 \in Z,\forall y \in x$
Hence we can say that, $f(x)$ is one-one and onto.
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Relations and Functions. Curated by Sachin Sharma. Free for all students.