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) = ((x+3)^2)/((x+3)(x-3)) = (x+3)/(x-3)`, which is the third expression