I am lost!! Find the inverse function of f(x)=log2(4x) Thanks

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  1. Remember the steps of finding the inverse.

    y = log2 (4x)

    step 1. interchange the x and y variables:
    x = log2 (4y)

    step2. solve this new equation for y
    x = log2 (4y) -----> 2^x = 4y , by definition
    y = (1/4)(2^x)
    = 2^-2 (2^x)
    = 2^(x-2)

    f^-1 (x) = 2^(x-2)


    change the original to exponential form:
    y = log2 (4x) ----> 2^y = 4x
    inverse ----> 2^x = 4y
    y = (1/4)(2^x) = 2^(x-2)

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