Let and be subsets of

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

X

and

Y

be subsets of

\mathbb{R}

, the set of real numbers. The function

f:X\to Y

defined by

f(x)=x^2

for

x\in X

is one-one but not onto if (here

\mathbb{R}^+

is the set of all positive real numbers) (a)

X=Y=\mathbb{R}^+

(b)

X=\mathbb{R},\ Y=\mathbb{R}^+

(c)

X=\mathbb{R}^+,\ Y=\mathbb{R}

(d)

X=Y=\mathbb{R}