Answer :
Final answer:
The correct number of one-to-one functions that satisfy the given equation is d) Functions 1, 2, and 3.
Explanation:
The number of one-to-one functions f:a,b,c,d → 0,1,2,...,10 such that 2f(a)-f(b)+3f(c)-f(d)=0 is:
a) 11
b) 20
c) 33
d) 44
In order to solve this equation, we can go through the given options and see which functions satisfy the equation. Let's go through each option:
a) 0 (2(9) + 2 - 20)/2 = 0
b) 4 (2(7) + 2 - 8)/2 = 4
c) 2 (2(5) +2 -1 -7)/2 = 2
d) 6 (2(9) + 1 - 7)/2 = 6
Based on the calculations, we can see that functions (a), (b), (c), and (d) all satisfy the equation. Therefore, the correct answer is d) Functions 1, 2, and 3.
