Q. 9

# Show that the fun

Answer :

(i) f : N N : f(x) = x2 is one - one into.

f(x) = x2

y = x2 Since the function f(x) is monotonically increasing from the domain N N

f(x) is one one

Range of f(x) = (0,∞)≠N(codomain)

f(x) is into

f : N N : f(x) = x2 is one - one into.

(ii) f : Z Z : f(x) = x2 is many - one into

f(x) = x2

y = x2

in this range the lines cut the curve in 2 equal valued points of y, therefore, the function f(x) = x2 is many - one .

Range of f(x) = (0,∞)≠Z(codomain)

f(x) is into f : Z Z : f(x) = x2 is many - one into

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