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7 September, 10:08

Given the function f (x) = log3 (x + 4), find the value of f-1 (3

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  1. 7 September, 12:39
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    First of all, find f ⁻¹ (x), or the inverse function like so:

    y = log (3x + 12)

    e^y = 3x + 12

    3x = e^y - 12

    x = 1/3 (e^y - 12)

    Now, swap x and y:

    f ⁻¹ (x) = y = 1/3 (e^x - 12)

    Secondly and finally, substitute 3 into this eq'n:

    f ⁻¹ (3) = 1/3 (e³ - 12) = 2.695 ...

    so 2.695 (to 4 sig. figs / 3 d. ps)

    or if asked for an exact answer then it is just: 1/3 (e³ - 12), which can be simplfied to 1/3e³ - 4.
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