Answer:
f(0)=11
Step-by-step explanation:
f(x) is a linear function, hence it is of the form f(x)=ax+b for some constants a,b.
When we divide f(x) by x-3 the remainder is 5. Moreover, using the division algorith we have that
hence 5=b+3a.
On the other hand, when we divide f(x) by x-4 the reminder is 3. Also, using the division algorithm, we have that
hence 3=b+4a.
Therefore, to find f(x), we have to solve the linear sistem
If we substract the first and the second equation, we get
and using the last result we get that
Hence, f(x)=-2x+11, and so f(0)=11.