SOLUTION: A function f is defined for integers m and n as given: {{{ f(mn) = f(m)*f(n)-f(m+n)+1001}}}, where either m or n is equal to 1, and f(1) = 2. a) Prove that {{{ f(x)=f(x-1)+1001}

Algebra ->  Functions -> SOLUTION: A function f is defined for integers m and n as given: {{{ f(mn) = f(m)*f(n)-f(m+n)+1001}}}, where either m or n is equal to 1, and f(1) = 2. a) Prove that {{{ f(x)=f(x-1)+1001}      Log On


   



Question 1145171: A function f is defined for integers m and n as given: +f%28mn%29+=+f%28m%29%2Af%28n%29-f%28m%2Bn%29%2B1001, where either m or n is equal to 1, and f(1) = 2.
a) Prove that +f%28x%29=f%28x-1%29%2B1001
b) Find the value of f(9999).

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A function f is defined for integers m and n as given:
+f%28mn%29+=+f%28m%29%2Af%28n%29-f%28m%2Bn%29%2B1001, where either m or n is equal to 1,
and f(1) = 2.
a) Prove that +f%28x%29=f%28x-1%29%2B1001
Let m = x-1 and n = 1



Edwin