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24 Dec 2024, 02:18
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As per the question \(f(f(x))=x^\frac{1}{4}\)
Let \(p\) be any prime number,
And \(x^\frac{1}{4}= \frac{1}{p}\)
so, \(x=\frac{1}{p^4}\)
solving each options
A. \(0.25= \frac{1}{4}\) eliminate
B. \(0.04= \frac{1}{25}\) eliminate
C. \(\frac{16}{1000}= \frac{2}{125}\) eliminate
D. \(\frac{8}{1000}= \frac{1}{125}\)= \(\frac{1}{5^3}\) eliminate
E.\( \frac{16}{10000}= \frac{1}{625}= \frac{1}{5^4}\) and 5 is also a prime number
Hence, E.
Let \(p\) be any prime number,
And \(x^\frac{1}{4}= \frac{1}{p}\)
so, \(x=\frac{1}{p^4}\)
solving each options
A. \(0.25= \frac{1}{4}\) eliminate
B. \(0.04= \frac{1}{25}\) eliminate
C. \(\frac{16}{1000}= \frac{2}{125}\) eliminate
D. \(\frac{8}{1000}= \frac{1}{125}\)= \(\frac{1}{5^3}\) eliminate
E.\( \frac{16}{10000}= \frac{1}{625}= \frac{1}{5^4}\) and 5 is also a prime number
Hence, E.
24 Dec 2024, 02:42
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To solve this, let's first compute f(f(x)).
f(f(x)) = √(√x) => x^(1/4).
Set x^(1/4) = 1/p, where p is a prime number.
x = (1/p)^4 = 1/p^4.
Now, Let's go through each option
A. 0.25 = 1/4 = 1/2^2 → Not valid.
B. 0.04 = 1/25 = 1/5^2 → Not valid.
C. 0.016 = 10/625 → Not Valid.
D. 0.008 = 1/125 = 1/5^3 → Not valid.
E. 0.0016 = 1/625 = 1/5^4 → Valid since p is a prime number in this case
Answer is E (0.0016).
f(f(x)) = √(√x) => x^(1/4).
Set x^(1/4) = 1/p, where p is a prime number.
x = (1/p)^4 = 1/p^4.
Now, Let's go through each option
A. 0.25 = 1/4 = 1/2^2 → Not valid.
B. 0.04 = 1/25 = 1/5^2 → Not valid.
C. 0.016 = 10/625 → Not Valid.
D. 0.008 = 1/125 = 1/5^3 → Not valid.
E. 0.0016 = 1/625 = 1/5^4 → Valid since p is a prime number in this case
Answer is E (0.0016).
24 Dec 2024, 04:13
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Considering all options leaves E
16/10000 = 4/100 = 2/10, which is the reciprocal of 5
16/10000 = 4/100 = 2/10, which is the reciprocal of 5
