Classify the following functions as injection, surjection or bije… - Vidyadip

Question

Classify the following functions as injection, surjection or bijection:
$f : N \rightarrow N$ given by $f(x) = x^2$

✓

Answer

$f : N \rightarrow N$ given by $f(x) = x^2$ Let $x_1 = x_2$ for
$\text{x}_1,\text{ x}_2\in\text{N}$$\text{x}_1^2=\text{x}_2^2\Rightarrow\ \text{f}(\text{x}_1)=\text{f}(\text{x}_2)$
$\therefore$ f is one-one.
Surjectivity: Since f takes only square value like $1, 4, 9, 16 ....$.
So, non-perfect square values in N $(\infty-\text{domain})$ do not have pre image in domain N.
Thus, f is not onto.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Functions→Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\int \cos ^7 x d x$

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ find $\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{a}}\big).$

Let * be a binary operation on set of integers I, defined by a * b = 2a + b − 3. Find the value of 3 * 4.

If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)

Evaluate the following integrals:$\int\limits^1_0\frac{1}{1+\text{x}^2}\text{ dx}$

Find the $n^{\text {th }}$ derivative of the following : $x^m$

Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On $R$, define * by $a$ * $b=a+4 b^2$
Here, $Z ^{+}$denotes the set of all non-negative integers.

Evaluate: $\int \frac{d \theta}{\sin \theta+\sin \theta}$

If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},$ find $A + A^T$.

Find the principal value of the following:
$\cos^{-1}\Big(\sin\frac{4\pi}{3}\Big)$