Question

Find (f/g) (x) and state the domain restriction. f (x) = 6x - 3 and g(x) = 12x^2 - 6x

Answer 1

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Answer:

(f/g)(x) = 1/(2x)

x ≠ 1/2

Explanation:

`(f/g)(x)=(f(x))/(g(x))=(6x-3)/(12x^2-6x)=(6x-3)/(2x(6x-3))\\\\\boxed{(f/g)(x)=(1)/(2x)}\quad x\\e(1)/(2)`

The domain restriction x ≠ 1/2 comes from the requirement to prevent the denominator factor 6x-3 from being zero.