Without using a calculator, answer the following:
On the interval 0 ≤ x ≤ 1, which graph, f(x) = x^(1/2) or g(x) = x^(1/4), generally results in higher values?
The answer is g(x), but why?
On the interval 0 ≤ x ≤ 1, which graph, f(x) = x^(1/2) or g(x) = x^(1/4), generally results in higher values?
The answer is g(x), but why?
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Consider x=1/2. The nominator is one and stays so no matter what 'root' is applied. The denominator (2) becomes smaller for the application of the higher 'root', i.e. x^(1/4); thus the quotient (1/2)^(1/4) is larger for this case.
Sorry, this is not a good or complete answer......I guess it could be adapted to complete the explanation.
Sorry, this is not a good or complete answer......I guess it could be adapted to complete the explanation.
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Hi,
It's because as you multiply decimals, the result becomes smaller rather than larger as is the case with whole numbers. This may be a little hard to see, so I'll give some examples.
Let's say we multiply .1*.1*.1*.1 that's .0001. But .1*.1 is just .01. So, if I take the 4th root of .0001, that's .1. But the number that I have to square to get .0001 is .01. That is .01*.01 is .0001. So, if I take the square root of .0001, it's .01. So, as we can see, the higher the root for a specific number the larger the result, since the result was increasing as the root index increased.
This is possible a little hard to see, but that's about the best I can do in a short period of time and not knowing what your math background is. Hope this has helped a little.
formeng
It's because as you multiply decimals, the result becomes smaller rather than larger as is the case with whole numbers. This may be a little hard to see, so I'll give some examples.
Let's say we multiply .1*.1*.1*.1 that's .0001. But .1*.1 is just .01. So, if I take the 4th root of .0001, that's .1. But the number that I have to square to get .0001 is .01. That is .01*.01 is .0001. So, if I take the square root of .0001, it's .01. So, as we can see, the higher the root for a specific number the larger the result, since the result was increasing as the root index increased.
This is possible a little hard to see, but that's about the best I can do in a short period of time and not knowing what your math background is. Hope this has helped a little.
formeng