Problem

Problem

Let

X

and

Y

be subsets of

\mathbb{R}

, the set of all real numbers. The function

f: X \rightarrow 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}

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