Ex 1.2, 4 - Show that Modulus Function f(x) = |x| is neither - To prove injective/ surjective/ bijective (one-one & onto)

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Ex 1.2 , 4 Show that the Modulus Function f: R R given by f(x) = , is neither one-one nor onto, where is x, if x is positive or 0 and is x, if x is negative. f(x) = = , 0 , <0 Check one-one For example: f (1) = 1 = 1 f ( 1) = 1 = 1 Check onto f: R R f(x) = Let f(x) = y such that y R y = Hence value of y is defined only if y is positive, But y is a real number Hence, if y is negative, there is not corresponding element of x Hence, f is not onto

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