Consider functions f and g.

f⁡(x) = x^2−16/x^2+3⁢x−10, for x≠-5 and x≠2
g⁡(x) = x^2−4/x^2−7⁢x+12, for x≠3 and x ≠4
What is (f(x))(g(x))

1 answer

To find (f(x))(g(x)), we need to multiply the functions f(x) and g(x).

(f(x))(g(x)) = (x^2 - 16/x^2 + 3x - 10)(x^2 - 4/x^2 - 7x + 12)

Multiplying these two polynomials gives:

(f(x))(g(x)) = x^4 - 4 + 3x^3 - 12x - 16/x^2 - 64/x^2 - 21x^2 + 84x - 30 - 48/x^2 + 60/x + 20/x - 120/x

Combining like terms, we get:

(f(x))(g(x)) = x^4 + 3x^3 - 21x^2 - 87x - 124 - 48/x^2 + 80/x - 40/x

Therefore, (f(x))(g(x)) = x^4 + 3x^3 - 21x^2 - 87x - 124 - 48/x^2 + 80/x - 40/x.