Question

Function Operations
Given the functions: f(x) = 6x + 3 and g(x) = x² + 10x - 7,

Answer 1

Part 1

`(f+g)(x)=f(x)+g(x) \\ \\ =(6x+3)+(x^2 +10x-7) \\ \\ =\boxed{x^2 + 16x-4}`

Part 2

`(f-g)(x)=f(x)-g(x) \\ \\ =(6x+3)-(x^2 +10x-7) \\ \\ =6x+3-x^2-10x+7 \\ \\ =\boxed{-x^2 - 4x+10}`

Part 3

`(f\cdot g)(x)=f(x) \cdot g(x) \\ \\ =(6x+3)(x^2 +10x-7) \\ \\ =6x^3 + 60x^2 - 42x+3x^2 + 30x-21 \\ \\ =\boxed{6x^3 + 63x^2 - 12x-21}`

Part 4

`\left((f(x))/(g(x)) \right)=(f(x))/(g(x)) \\ \\ =\boxed{(x^2 + 10x-7)/(6x+3)}`