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1. Conslaer the Curve y =JX) = 2"-1.

A. Find the exact area of the region in the first quadrant bounded by the curves y = fx) = 2-1
and y = x. ("Exact area" means no calculator numbers.)
B. Find the inverse function y =flx).
C. Using part A and the notion of symmetry between a function and its inverse, find the exact
area of the region in the first quadrant bounded by the curves y = flx) and y = x. Explain your
reasoning. (Hint: Think "graphically" and little or no math will need to be done!)

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1 answer
  1. No idea what y =JX) = 2"-1 is.
    If you mean y = 2^x - 1
    then
    (A) the area on the interval [1,2] is
    ∫[1,2] x-(2^x - 1) dx
    (B) f-1(x) = log2(x+1)
    (C) see what you can do with this.
    If you actually meant y = 2^(x-1) then make the appropriate adjustments

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