Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 5"
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− | Suppose that <math>f</math> is a function with the property that for all <math>x</math> and <math>y, f(x + y) = f(x) + f(y) + 1</math> and <math>f(1) = 2.</math> What is the value of <math>f(3)</math>? | + | Suppose that <math>f</math> is a function with the property that for all <math>x</math> and <math>y</math>, <math>f(x + y) = f(x) + f(y) + 1</math> and <math>f(1) = 2.</math> What is the value of <math>f(3)</math>? |
<center><math> \mathrm{(A) \ }4 \qquad \mathrm{(B) \ }5 \qquad \mathrm{(C) \ }6 \qquad \mathrm{(D) \ }7 \qquad \mathrm{(E) \ }8 </math></center> | <center><math> \mathrm{(A) \ }4 \qquad \mathrm{(B) \ }5 \qquad \mathrm{(C) \ }6 \qquad \mathrm{(D) \ }7 \qquad \mathrm{(E) \ }8 </math></center> |
Revision as of 14:51, 29 July 2006
Problem
Suppose that is a function with the property that for all
and
,
and
What is the value of
?
![$\mathrm{(A) \ }4 \qquad \mathrm{(B) \ }5 \qquad \mathrm{(C) \ }6 \qquad \mathrm{(D) \ }7 \qquad \mathrm{(E) \ }8$](http://latex.artofproblemsolving.com/e/7/1/e719d0dae853a231d3f6f4ffaeeb56648c1f073b.png)
Solution
Notice that . Also,
. Thus,
.