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If f(x) = 2x - 1/x for x>0 and g is the inverse of f, then what is the value of g’(0)View attachment 15139

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It looks like you are finding the value of g(0), that is, x such that f(x) = 0. That's good.If f(x) = 2x - 1/x for x>0 and g is the inverse of f, then what is the value of g’(0)

What have you learned about the derivative of an inverse function? What have you done on that part of the problem?

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Here is the idea. Use implicit differentiation:

\(\displaystyle g(f(x))=x\\g'(f(x))\cdot f'(x)=1\\g'(f(x))=\dfrac{1}{f'(x)}\)

Now you need \(\displaystyle f(?)=0\)

I just need the correct answer because the answer I got what different compare to my teacher.

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What answer did you get? More importantly,"I just need the correct answer because the answer I got what different compare to my teacher."

HOW did you get it?

Show us - so that we can show you the correct way!

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We can read. But we wanted you to provide some of your work so that we can see if you need help understanding the concepts incolved, Prof Peterson asked you about your knowledge of the inverse function. You completely ignored his request. WHY?

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