Math 1201 unit 5 discussion post part 11.docx - The inverse...

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The inverse mentioned in the question is not the regular inverse, meaning if we have a functionf(x)=x n then its inverse is not f-1(x)=x-n.the inverse in the following way,f(x)=xnx=f-1(xn)x=f-n(x)x= [ f-1(x) ]nx n 1= [ f-1(x) ]f-1(x)=x1/nSo for the function f(x)=x3, as per above discussion , f-1(x)=x1/3. Now If we plot the functions f(x)and f'(x) on the same graph with same X-axis using "desmos" we get the following graph,Here, the red curve is y=x3and blue curve is y=x1/3and the green line is y=x.As the red curve and blue curves can be seen there are a reflection or reflecting pictures aboutthe y=x line of the field {-2<x<2}. This also shows us the one-to-one relationship between the twofunctions. But the difficulty with the same graph with the same x-axis is that, in the given domain,the f(x) function does not have the same range and it is inversely. In the sense that we have
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Term
Spring
Professor
NoProfessor
Tags
Inverse function, Injective function, Graph of a function

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