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anonymous

  • one year ago

This confuses me, please help.

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @dan815 any help?

  3. iGreen
    • one year ago
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    \(\sf f(\dfrac{1}{2})\) means to plug in 1/2 for 'x'

  4. iGreen
    • one year ago
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    \(\sf f(x) = 3^x\) \(\sf f(\dfrac{1}{2}) = 3^{\frac{1}{2}}\)

  5. iGreen
    • one year ago
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    Simplify the right side.

  6. anonymous
    • one year ago
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    1.5, right?

  7. iGreen
    • one year ago
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    No..1/2 is an exponent, it's not being multiplied. \(\sf 3^{\frac{1}{2}} \rightarrow 3^{0.5}\)

  8. iGreen
    • one year ago
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    Plug it in your calculator

  9. anonymous
    • one year ago
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    I do not have one, but would it be 1/3 of 3^0.5?

  10. iGreen
    • one year ago
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    Well, you can't really do this without a calculator.

  11. iGreen
    • one year ago
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    \(\sf a^{\frac{n}{m}} \rightarrow \sqrt[m]{a^n}\)

  12. iGreen
    • one year ago
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    So basically we're looking at: \(\sf \sqrt[2]{3^1} \rightarrow \sqrt{3}\)

  13. iGreen
    • one year ago
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    \(\sf \sqrt{3} \approx 1.73205081.~.~.\)

  14. iGreen
    • one year ago
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    Now can you do the same with \(\sf f(\dfrac{1}{4})\)?

  15. anonymous
    • one year ago
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    I can try.

  16. anonymous
    • one year ago
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    I got 1.31607401 from the calculator I just got.

  17. iGreen
    • one year ago
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    Yep! \(\sf f(\dfrac{1}{4}) \rightarrow f(\dfrac{1}{4}) = 3^{\frac{1}{4}} \rightarrow \sqrt[4]{3^1} \rightarrow \sqrt[4]{3} \rightarrow 1.31607401.~.~.\)

  18. iGreen
    • one year ago
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    Don't forget to round both of them to the nearest hundredth.

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