To find (f⋅g)(x), we need to multiply the functions f(x) and g(x) together.
First, rewrite f(x) and g(x) in factored form:
f(x) = (x-2)(x+2)/(x-2)(x+5)
g(x) = (x-3)(x-1)/(x-4)(x-3)
Now we can cancel out common factors between numerator and denominator:
f(x) = (x+2)/(x+5)
g(x) = (x-1)/(x-4)
Next, multiply the two functions together:
(f⋅g)(x) = (x+2)/(x+5) * (x-1)/(x-4)
To multiply these fractions, we multiply the numerators together and the denominators together:
(f⋅g)(x) = (x+2)(x-1)/((x+5)(x-4))
Expanding the numerator and the denominator:
(f⋅g)(x) = x^2 + x - 2)/(x^2+x-20)
So, (f⋅g)(x) = x^2+x-2)/(x^2+x-20).
Consider functions f and g.
f(x) = x^2−16/x^2+3x−10, for x≠-5 and x≠2
g(x) = x^2−4/x^2−7x+12, for x≠3 and x ≠4
What is (f⋅g)(x)?
1 answer