Onto Function or Surjective MCQ - Practice Questions & Answers

Solve by difficulty

EASY

$f : (- \infty, \infty) \to [0, \infty), f (x) = x^{2}$ is a/an:

One-one function

Onto function

Into function

Bijective function

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Find the number of onto functions from $A$ to $B$ where $n (A) = 5$ and $n (B) = 3$ .

243

^{$^{5} P_{3}$}

160

150

View Solution

Concepts Covered - 1

Onto Function or Surjective

A function $f : X \to Y$ is said to be onto (or surjective), if every element of $Y$ is the image of some element of $X$ under $f$ , i.e., for every $y \in Y$ , there exists an element $x$ in $X$ such that $f (x) = y$

Hence, Range = co-domain for an onto function

Some examples of onto function
Consider, $X = {x_{1}, x_{2}, x_{3}, x_{4}}$ and $Y = {y_{1}, y_{2}, y_{3}} ∣$

$f : X \to Y$

As every element in Y has a pre-image in X, so it is an onto function

Method to show onto or surjective

Find the range of $y = f (x)$ and show that range of $f (x) =$ co-domain of $f (x)$

Number of onto functions $= \sum_{r=1}^{n}\left ( -1 \right )^{n-r}n_{C_{r}}r^{m}$

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