Difference between revisions of "1975 AHSME Problems/Problem 21"
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| − | + | ==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</math> and <math>b</math>. Which of the following statements are true? | 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</math> and <math>b</math>. Which of the following statements are true? | ||
Revision as of 16:40, 19 January 2021
Problem
Suppose 
is defined for all real numbers 
for all 
and 
for all 
and 
. Which of the following statements are true?
![$I.\ f(0) = 1 \qquad \qquad \ \ \qquad \qquad \qquad II.\ f(-a) = \frac{1}{f(a)}\ \text{for all}\ a \\ III.\ f(a) = \sqrt[3]{f(3a)}\ \text{for all}\ a \qquad IV.\ f(b) > f(a)\ \text{if}\ b > a$](http://latex.artofproblemsolving.com/4/d/9/4d99396f9b9df7af48fb5457e20daa4ddc94ad70.png)
Solution
nothing yet :(
See Also
| 1975 AHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
