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Plugin Problem - # 3
- Thread starter Jason76
- Start date
Make sure you didn't mistype 2/3 and wrote 3/2 instead, as this wouldn't work for obvious reasons, unless your computer can do complex calculations.
Else well, I don't know, sorry.
No, I wrote the problem correctly.
D
Deleted member 4993
Guest
\(\displaystyle f(x) = 16 - x^{2/3}\)
\(\displaystyle f(-64) = 16 - (-64)^{2/3} = ?\)
??? Undefined (but the computer says that's wrong). On calculator it just gives -E- for \(\displaystyle (-64)^{2/3}\)
\(\displaystyle f(-64) = 16 - (-64)^{2/3} = ?\)
\(\displaystyle f(-64) = 16 - [(-64)^{\frac{1}{3}}]^2 = ?\)
\(\displaystyle f(-64) = 16 - [-4]^2 = ?\)
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
YOU are supposed to be smarter than a calculator! Don't just use one mindlessly.
You should know that, while even roots of negative numbers are not defined, odd roots are. I suspect that your calculator is taking fractional roots, \(\displaystyle x^{1/n}\), by calculating the exponential of (1/n) ln(x). And ln(x) is not defined for x negative or 0. Your calculators manual probably mentions that. Find the third root of +64. Since you are squaring that the sign does not matter.
(Of course, this also has two non-real complex solutions. Are you only asked for the real one?)
You should know that, while even roots of negative numbers are not defined, odd roots are. I suspect that your calculator is taking fractional roots, \(\displaystyle x^{1/n}\), by calculating the exponential of (1/n) ln(x). And ln(x) is not defined for x negative or 0. Your calculators manual probably mentions that. Find the third root of +64. Since you are squaring that the sign does not matter.
(Of course, this also has two non-real complex solutions. Are you only asked for the real one?)