Difference between revisions of "1975 AHSME Problems/Problem 21"

(Created page with "te==Problem== Suppose <math>f(x)</math> is defined for all real numbers <math>x; f(x) > 0</math> for all <math>x;</math> and <math>f(a)f(b) = f(a + b)</math> for all <math>a</...")
 
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\textbf{(E)}\ \text{All are true.}
 
\textbf{(E)}\ \text{All are true.}
 
</math>
 
</math>
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==Solution==
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nothing yet :(
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==See Also==
 
==See Also==
 
{{AHSME box|year=1975|num-b=20|num-a=22}}
 
{{AHSME box|year=1975|num-b=20|num-a=22}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 16:39, 19 January 2021

te==Problem== Suppose $f(x)$ is defined for all real numbers $x; f(x) > 0$ for all $x;$ and $f(a)f(b) = f(a + b)$ for all $a$ and $b$. Which of the following statements are true?

$I.\ f(0) = 1 \qquad \qquad \ \  \qquad \qquad \qquad II.\ f(-a) = \frac{1}{f(a)}\ \text{for all}\ a \\ III.\ f(a) = \sqrt[3]{f(3a)}\ \text{for all}\ a \qquad IV.\ f(b) > f(a)\ \text{if}\ b > a$

$\textbf{(A)}\ \text{III and IV only} \qquad \textbf{(B)}\ \text{I, III, and IV only} \\ \textbf{(C)}\ \text{I, II, and IV only} \qquad \textbf{(D)}\ \text{I, II, and III only} \qquad \textbf{(E)}\ \text{All are true.}$


Solution

nothing yet :(


See Also

1975 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

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