Difference between revisions of "1974 AHSME Problems/Problem 12"
(Created page with "==Problem== If <math> g(x)=1-x^2 </math> and <math> f(g(x))=\frac{1-x^2}{x^2} </math> when <math> x\not=0 </math>, then <math> f(1/2) </math> equals <math> \mathrm{(A)\ } 3/4 \...") |
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==See Also== | ==See Also== | ||
{{AHSME box|year=1974|num-b=11|num-a=13}} | {{AHSME box|year=1974|num-b=11|num-a=13}} | ||
| + | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 12:43, 5 July 2013
Problem
If 
and 
when 
, then 
equals
Solution
Notice that if we can find a 
such that 
, then we can plug that into the second equation to get 
. Thus, we let 
. Notice that, since our final expression only involves 
, we don't need to take the square root. Thus, 
.
See Also
| 1974 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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. 
