Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

Given f^-1(x)= 1100(1.02)^x, Solve f(x)=0?

Solve please show work

1 Answer

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  • 7 years ago
    Best Answer

    This is the inverse-function, so first we need to find the function.

    f⁻¹(x) = 1100(1.02)ˣ

    y = 1100(1.02)ˣ

    switch x and y

    x = 1100(1.02)^y

    x/1100 = 1.02^y

    log(x/1100) = log(1.02^y)

    log(x/1100) = y·log(1.02)

    y = log(x/1100)/log(1.02)

    f(x) = log(x/1100)/log(1.02)

    now let f(x) = 0 and solve for x:

    0 = log(x/1100)/log(1.02)

    0·log(1.02) = log(x/1100)

    0 = log(x/1100)

    10⁰ = 10^(log(x/1100))

    1 = x/1100

    x = 1100

    __________________

    Source(s): Math Tutor A.A. Math & Science ----------------------------- I will block users who do not choose a Best Answer themselves. I block them so I remember not to help them.
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