For (x+3) → (f/g)(x), for x^3-15x^2+27x+243 → (f.g)(x), for x^2-5x-36 → (f+g)(x), for x^2-7x -18 → (f-g)(x) represents correct combination.
What is a function?
It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
[tex]\rm f(x) = x^2-6x-27[/tex] and
[tex]\rm g(x) = x-9[/tex]
[tex]\rm (f+g)x = x^2-6x-27+x-9\\\\(f+g)x = x^2-5x-36[/tex]
[tex]\rm \dfrac{f}{g}(x) = \dfrac{x^2-6x-27}{x-9}\\\\\\rm \dfrac{f}{g}(x) = \dfrac{(x+3)(x-9)}{x-9}\\\\\rm \dfrac{f}{g}(x) = x+3[/tex]
[tex]\rm (f\times g)(x) = (x^2-6x-27)(x-9)\\\\\rm (f\times g)(x) =x^3-15x^2+27x+243[/tex]
[tex]\rm (f-g) = x^2-6x-27-(x-9)\\\\\rm (f-g) =x^2-7x -18[/tex]
Thus, for (x+3) → (f/g)(x), for x^3-15x^2+27x+243 → (f.g)(x), for x^2-5x-36 → (f+g)(x), for x^2-7x -18 → (f-g)(x) represents correct combination.
Learn more about the function here:
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