Sure, no problem. Let's go step by step:
First Pair:
1. f(x) = 3x-6 and g(x) = -4x+7.
Adding: (3x-6) + (-4x+7) results in -x+1;
Subtracting: (3x-6) - (-4x+7) results in 7x-13;
Multiplying: (3x-6) * (-4x+7) results in -12x^2+21x+42; and
Dividing: (3x-6) / (-4x+7) results in -(3x-6)/(4x-7).
Second Pair:
2. f(x) = 5x+2 and g(x) = 8-2x.
Adding: (5x+2) + (8-2x) results in 3x+10;
Subtracting: (5x+2) - (8-2x) results in 7x-6;
Multiplying: (5x+2) * (8-2x) results in -10x^2 + 40x + 16; and
Dividing: (5x+2) / (8-2x) results in (5x+2)/(2x-8).
Third Pair:
3. f(x) = x-16 and g(x) = x^2+16.
Adding: (x-16) + (x^2+16) results in x^2+x;
Subtracting: (x-16) - (x^2+16) results in x^2 + x - 32;
Multiplying: (x-16) * (x^2+16) results in x^3 - 16x^2 + 16x; and
Dividing: (x-16) / (x^2+16) results in (x-16)/(x^2+16).
Fourth Pair:
4. f(x) = 2x+3 and g(x) =x^2-14x.
Adding: (2x+3) + (x^2-14x) results in x^2 -12x + 3;
Subtracting: (2x+3) - (x^2-14x) results in -x^2 + 16x + 3;
Multiplying: (2x+3) * (x^2 - 14x) results in 2x^3 - 28x^2 + 3x; and
Dividing: (2x+3) / (x^2-14x) results in (2x+3)/(x^2-14x).
So, these are the respective operations applied on each pair of functions.