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Show that the Modulus Function f : R → R, given by f(x) = | x |, is neither one-one nor onto, where | x | is x, if x is positive or 0 and |x | is – x, if x is negative.
Show that the Modulus Function f : R → R, given by f(x) = | x |, is neither one-one nor onto, where | x | is x, if x is positive or 0 and |x | is – x, if x is negative.
CBSE | Class 12 | Maths | NCERT | Relations and Functions
Show that the Modulus Function f : R → R, given by f(x) = | x |, is neither one-one nor onto, where | x | is x, if x is positive or 0 and |x | is – x, if x is negative.

solution:

f : R → R, given by f(x) = | x |, characterized as

f contains values like (- 1, 1),(1, 1),(- 2, 2)(2,2)

f(- 1) = f(1), yet – 1

f isn’t one-one.

R contains some adverse numbers which are not pictures of any genuine number since f(x) = |x| is consistently non-negative. So f isn’t onto.

Henceforth, Modulus Function is neither one-one nor onto.

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