Re: If f is a fraction between −1 and 1, which of the following
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03 Feb 2020, 09:35
A: f^7 < f^5 when f is a positive fraction, but when f is negative, f^7 has the smaller absolute value or in other words, is the smaller negative number of the two and therefore greater than f^5 --> not always the case
B: rewrite in f^6*(1-f) < f^4 (1-f) | : (1-f) --> sign doesn't change, since 1-f is always positive (if f is positive, then 0< 1-f < 1 and if f is negative (=-f): 1< 1-(-f) <2)
-->f^6 < f^4 --> f^6 is always smaller than f^4 bc. both have even exponents and thus are positive;
--> CORRECT
C: see B) f^6*(1+f) < f^4*(1+f) --> f^6 is always smaller than f^4 bc. both have even exponents and thus are positive
--> CORRECT
D: if f is a positive fraction, the statement is correct, but if f is negative, -f^3 is positive and therefore greater
E: see B and C: f^6 is always smaller than f^4 bc. both have even exponents and thus are positive (a positive fraction gets smaller, the higher the exponent)
--> CORRECT
--> B, C and E are correct