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Bijective Function

Let f: Z → ...

Question

Let $f : Z \to Z$ be defined as $f (x) = x^{2}, x ϵ Z$ . What is the $f$ ?

A

A bijection

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B

An injection

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C

A surjection

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D

A function

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Solution

The correct option is B A function
$f (x) = x^{2}$
Graph of $f (x)$ is shown in the figure.
If we draw any line parallel to $y$ axis, it cuts the graph at only one point.
So, it represents a function.
Hence, option D is correct.

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Similar questions

f : Z

\to

Z

be defined as f(x)

= x^{2}, x \in Z

f

Q. Find whether the following function are onto or not:

f : Z \to Z

f (x) = 6 x - 7

x ϵ Z

Q. Classify the following functions as injection, surjection or bijection :
(i) f : N → N given by f(x) = x²
(ii) f : Z → Z given by f(x) = x²
(iii) f : N → N given by f(x) = x³
(iv) f : Z → Z given by f(x) = x³
(v) f : R → R, defined by f(x) = |x|
(vi) f : Z → Z, defined by f(x) = x² + x
(vii) f : Z → Z, defined by f(x) = x − 5
(viii) f : R → R, defined by f(x) = sinx
(ix) f : R → R, defined by f(x) = x³ + 1
(x) f : R → R, defined by f(x) = x³ − x
(xi) f : R → R, defined by f(x) = sin²x + cos²x
(xii) f : Q − {3} → Q, defined by

f (x) = \frac{2 x + 3}{x - 3}

(xiii) f : Q → Q, defined by f(x) = x³ + 1
(xiv) f : R → R, defined by f(x) = 5x³ + 4
(xv) f : R → R, defined by f(x) = 3 − 4x
(xvi) f : R → R, defined by f(x) = 1 + x²
(xvii) f : R → R, defined by f(x) =

\frac{x}{x^{2} + 1}

[NCERT EXEMPLAR]

Q. Check the injectivity and surjectivity of the following functions:

f : Z \to Z

f (x) = x^{2}

f : Z \to Z

f (x) = x^{2}

f

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