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29 May, 12:23

46. The function f graphed above is the function f (x) = log2 (x) + 2 for x > 0. Find a formula for the inverse of this function.

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  1. 29 May, 12:45
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    The inverse for log₂ (x) + 2 is - log₂x + 2.

    Step-by-step explanation:

    Given that

    f (x) = log₂ (x) + 2

    Now to find the inverse of any function we put we replace x by 1/x.

    f (x) = log₂ (x) + 2

    f (1/x) = g (x) = log₂ (1/x) + 2

    As we know that

    log₂ (a/b) = log₂a - log₂b

    g (x) = log₂1 - log₂x + 2

    We know that log₂1 = 0

    g (x) = 0 - log₂x + 2

    g (x) = - log₂x + 2

    So the inverse for log₂ (x) + 2 is - log₂x + 2.
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