08 Continuity and Differentiability

08 Continuity and Differentiability - f(g(x)) x 8....

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Unformatted text preview: f(g(x)) x 8. CONTINUITY AND DIFFERENTIABILITY 1. The functions f and g are given by 2 ) 3 ( ) ( 3 ) ( x x g and x x f- =- = (a) [5 marks] Show that the function defined by y = f (g(x)) is defined for all real values of x and sketch its graph. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 40 8. Continuity and Differentiability (b)[2 marks] For what values of x is k the derivative of this function undefined? Justify your answer. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [2 marks] Find the derivative of this function for all values of x where it exists. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (d)[1 mark] How can the domain of g be changed in order that f and g become inverse functions?...
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08 Continuity and Differentiability - f(g(x)) x 8....

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