Ex 1.2 , 4 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. f(x) =|𝑥| = {█( 𝑥 , 𝑥≥0 @−𝑥 , 𝑥<0)┤ Check one-one Example f (1) = |1| = 1 f (– 1) = |1| = 1 Since, different elements 1, –1, have the same image 1 , ∴ f is not one-one. Check onto f: R → R f(x) = |𝑥| Let f(x) = y such that y ∈ R y = |𝑥| 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.