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29 Oct 2024, 01:30
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D
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Difficulty:
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Question Stats:
67% (02:17) correct
33%
(01:59)
wrong
based on 210
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For which of the following function is \(f(a - b) = \frac{f (a)}{f(b)}\) for all numbers a and b?
A. \(f(x) = x^3\)
B. \(f(x) = |5x+1|\)
C. \(f(x) = \frac{4x}{3-x}\)
D. \(f(x) = 2^{−3x}\)
E. \(f(x) = -1\)
A. \(f(x) = x^3\)
B. \(f(x) = |5x+1|\)
C. \(f(x) = \frac{4x}{3-x}\)
D. \(f(x) = 2^{−3x}\)
E. \(f(x) = -1\)
29 Oct 2024, 03:37
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A. \((a-b)^3 \neq \frac{a^3}{b^3}\) .... (i could no remember what \((a-b)^3\) formula is , but i don't think it can result in \(\frac{a^3}{b^3}\) , so took an educated guess and moved on)
B. \(|5a-5b+1|\neq |5a+1|/|5b+1|\)
C. \(\frac{4(a-b)}{3-a+b} \neq \frac{4a}{3-a} * \frac{3-b}{3b}\) ... after solving this a little ahead also this wont be equal
D. \(2^{-3(a-b)}\) is equal to \(\frac{2^{-3a}}{2^{-3b}}\) = \(2^{-3a+3b}\) = \(2^{-3(a-b)}\) .... LHS=RHS
I did not check for E while solving, coz D already was the answer. But for E:
E. \((a-b)= -1 \neq a= -1, b= -1\) ..... \(\frac{a}{b}= 1\) ... so not equal.
I think D.
B. \(|5a-5b+1|\neq |5a+1|/|5b+1|\)
C. \(\frac{4(a-b)}{3-a+b} \neq \frac{4a}{3-a} * \frac{3-b}{3b}\) ... after solving this a little ahead also this wont be equal
D. \(2^{-3(a-b)}\) is equal to \(\frac{2^{-3a}}{2^{-3b}}\) = \(2^{-3a+3b}\) = \(2^{-3(a-b)}\) .... LHS=RHS
I did not check for E while solving, coz D already was the answer. But for E:
E. \((a-b)= -1 \neq a= -1, b= -1\) ..... \(\frac{a}{b}= 1\) ... so not equal.
I think D.
General Discussion
03 Nov 2024, 06:43
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The answer is D.
A. f(a - b) = (a - b)^3 ; f(a)/f(b) = a^3/b^3. Not equal.
B. f(a - b) = |5(a - b) + 1| = |5a - 5b + 1| ; f(a)/f(b) = |5a + 1|/|5b + 1|. Not equal.
C. f(a - b) = 4(a - b)/(3 - (a - b)) = (4a - 4b)/(3 - a + b) ; f(a)/f(b) = [4a/(3 - a)]/[4b/(3 - b)] = 4a(3 - b)/4b(3 - a). Not equal.
D. f(a - b) = 2^[-3(a - b)] = 2^(-3a + 3b) = 2^(-3a)*2^3b = 2^3b/2^3a ; f(a)/f(b) = 2^(-3a)/2^(-3b) = 2^3b/2^3a. Equal.
E. f(a - b) = -1 ; f(a)/f(b) = -1/-1 = 1. Not equal.
A. f(a - b) = (a - b)^3 ; f(a)/f(b) = a^3/b^3. Not equal.
B. f(a - b) = |5(a - b) + 1| = |5a - 5b + 1| ; f(a)/f(b) = |5a + 1|/|5b + 1|. Not equal.
C. f(a - b) = 4(a - b)/(3 - (a - b)) = (4a - 4b)/(3 - a + b) ; f(a)/f(b) = [4a/(3 - a)]/[4b/(3 - b)] = 4a(3 - b)/4b(3 - a). Not equal.
D. f(a - b) = 2^[-3(a - b)] = 2^(-3a + 3b) = 2^(-3a)*2^3b = 2^3b/2^3a ; f(a)/f(b) = 2^(-3a)/2^(-3b) = 2^3b/2^3a. Equal.
E. f(a - b) = -1 ; f(a)/f(b) = -1/-1 = 1. Not equal.
