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find the inverse of the following function. Find the domain, range,and asymptotes of each function. Graph both functions on the same coordinate plane.

  • Pre-Cal. -

    y = 3 + lnx
    first step in finding the inverse is to interchange the x and y variables, so

    inverse is
    x = 3 + lny
    x-3 = lny
    y = e^(x-3)

    in original y = 3 + lnx
    domain , x > 0 , y is any real number

    so in the inverse these two would be interchanged.

    remember , when graphing an inverse of a function, you get a reflection in the line y = x

    in original, let x = 5
    y = 3+ln5 = 4.6094... (I stored it in memory)

    in inverse:
    x = 4.6094
    y = e^(1.6094) = 5

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