Let f be a linear function. when f x( ) is divided by x − 3, the remainder is 5. when f x( ) is divided by x − 4, the remainder is 3. what is the value of f ( ) 0 ?

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.

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