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3 Investigate the restrictions that should be applied to the domain of a cubic function...

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Algebra

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3 Investigate the restrictions that should be applied to the domain of a cubic function so that it has an inverse Sketch a cubic function g x x 4x 2 Is this a one to one function Explain your answer If the domain is restricted between x a and x b where both a and b are finite real numbers the function becomes one to one Find the largest possible domain a b Use the idea from the cubic function and investigate the domain and range of all the inverse trigonometric functions Use the following as a guideline for investigating other trigonometric functions too Sketch the graph of y sin x Find the largest possible domain for which the inverse can exist Find the domain and range of sin x Sketch both y sin x and y sin 1 x within the restricted domain

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