The function F(x) = x5 +2x + x is an increasing function (since F'(x) = 5x...

   

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The function F(x) = x5 +2x³ + x is an increasing function (since F'(x) = 5x² +6x² +1 > 0 ) and therefore has an inverse, which we denote as F-¹(x). (a) Use Matab to plot F(x) and F-1(x) on the same set of axes, with −1 ≤ x ≤ 1. (b) Write a Matlab function, whose prototype is y = inverseF(x). Here the input x is assumed such that −1 ≤ x ≤ 1, and the output y is the value of F-¹(x), correct to at least 7 significant digits. Discuss which numerical methods you used and how you guarantee the accuracy of your results. The function F(x) = x5 +2x³ + x is an increasing function (since F'(x) = 5x² +6x² +1 > 0 ) and therefore has an inverse, which we denote as F-¹(x). (a) Use Matab to plot F(x) and F-1(x) on the same set of axes, with −1 ≤ x ≤ 1. (b) Write a Matlab function, whose prototype is y = inverseF(x). Here the input x is assumed such that −1 ≤ x ≤ 1, and the output y is the value of F-¹(x), correct to at least 7 significant digits. Discuss which numerical methods you used and how you guarantee the accuracy of your results.