anonymous
  • anonymous
This confuses me, please help.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
@dan815 any help?
iGreen
  • iGreen
\(\sf f(\dfrac{1}{2})\) means to plug in 1/2 for 'x'

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iGreen
  • iGreen
\(\sf f(x) = 3^x\) \(\sf f(\dfrac{1}{2}) = 3^{\frac{1}{2}}\)
iGreen
  • iGreen
Simplify the right side.
anonymous
  • anonymous
1.5, right?
iGreen
  • iGreen
No..1/2 is an exponent, it's not being multiplied. \(\sf 3^{\frac{1}{2}} \rightarrow 3^{0.5}\)
iGreen
  • iGreen
Plug it in your calculator
anonymous
  • anonymous
I do not have one, but would it be 1/3 of 3^0.5?
iGreen
  • iGreen
Well, you can't really do this without a calculator.
iGreen
  • iGreen
\(\sf a^{\frac{n}{m}} \rightarrow \sqrt[m]{a^n}\)
iGreen
  • iGreen
So basically we're looking at: \(\sf \sqrt[2]{3^1} \rightarrow \sqrt{3}\)
iGreen
  • iGreen
\(\sf \sqrt{3} \approx 1.73205081.~.~.\)
iGreen
  • iGreen
Now can you do the same with \(\sf f(\dfrac{1}{4})\)?
anonymous
  • anonymous
I can try.
anonymous
  • anonymous
I got 1.31607401 from the calculator I just got.
iGreen
  • iGreen
Yep! \(\sf f(\dfrac{1}{4}) \rightarrow f(\dfrac{1}{4}) = 3^{\frac{1}{4}} \rightarrow \sqrt[4]{3^1} \rightarrow \sqrt[4]{3} \rightarrow 1.31607401.~.~.\)
iGreen
  • iGreen
Don't forget to round both of them to the nearest hundredth.

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