1.

If f : R → R be a function defined by f(x) = x2, show that the function f is many one into.

Answer»

f(x) = x2

f(x1) = f(x2)

x12 = x22

x12 - x22

(x1 - x2) (x1 + x2) = 0

Squaring x1 - x2 = 0 

x1 = x2

or, x1 = x2

or, x1 + x2 = 0

x1 = -x1

Hence, the function is many to one onto function.



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