Let X and Y be subsets of R, the set of all real numbers. The function f:X→Y defined by f(x)=x2 , x∈X is one-one but not onto if

f:X→Y defined by f(x)=x2 for x∈X is one-one but not into if X=R+,Y=R then Range of f is R+⊂R Negative elements does not have pre images in ‘X’

Let X and Y be subsets of R, the set of all real numbers. The function f:X→Y defined by f(x)=x2 , x∈X is one-one but not onto if

f:X→Y defined by f(x)=x2 for x∈X is one-one but not into if X=R+,Y=R then Range of f is R+⊂R Negative elements does not have pre images in ‘X’

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Let X and Y be subsets of R, the set of all real numbers. The function $f : X \to Y$ defined by $f (x) = x^{2}$ , $x \in X$ is one-one but not onto if

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X = Y = R^{+}

X = R, Y = R^{+}

X = R^{+}, Y = R

X = Y = R

answer is C.

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Detailed Solution

f : X \to Y

defined by

f (x) = x^{2}

for

x \in X

is one-one but not into if

X = R^{+}, Y = R

then Range of

f

R^{+} \subset R

Negative elements does not have pre images in ‘X’

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Let X and Y be subsets of R, the set of all real numbers. The function f:X→Y defined by f(x)=x2 , x∈X is one-one but not onto if

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Let X and Y be subsets of R, the set of all real numbers. The function $f : X \to Y$ defined by $f (x) = x^{2}$ , $x \in X$ is one-one but not onto if