= 1. (a) Let f : IR→IR be the function defined by f(x) = x4 – 4x2 for any x E IR. i. Is f injective? Justify your answer

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1 A Let F Ir Ir Be The Function Defined By F X X4 4x2 For Any X E Ir I Is F Injective Justify Your Answer 1 (132.01 KiB) Viewed 76 times

= 1. (a) Let f : IR→IR be the function defined by f(x) = x4 – 4x2 for any x E IR. i. Is f injective? Justify your answer. ii. Is f surjective? Justify your answer. (b) Verify that for any x € (V2, +0), x4 – 4x2 > -4. (c) Let g:(V2, +00) +, +(-4, +co) be the function defined by g(x) = x4 – 4.x2 for any x € (V2, +00). i. Is g injective? Justify your answer. ii. Is g surjective? Justify your answer. iii. Is g bijective? If yes, also write down the 'formula of definition' for its inverse function. - =