Question

Find the results combining these functions.

Answer 1

Given $f(x) = x^2 + 6x + 9, g(x) = x^2 - 9$:

$(f+g)(x) = (x^2 + 6x+9)+(x^2-9) =2x^2+6x=2x(x+3)$, which is the second expression

$(f-g)(x) = (x^2 + 6x+9)-(x^2-9) =6x+18=6(x+3)$, which is the first second expression

$(fxg)(x) = (x^2+6x+9)(x^2-9) = (x^4-9x^2)+(6x^3-54x)+(9x^2-81)=x^4+6x^3-54x-81$, which is the fourth expression

$(f/g)(x) = (x^2+6x+9)/(x^2-9) = \frac{(x+3)^2}{(x+3)(x-3)} = \frac{x+3}{x-3}$, which is the third expression