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

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Answer:

  (f/g)(x) = 1/(2x)

  x ≠ 1/2

Step-by-step explanation:

  [tex](f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{6x-3}{12x^2-6x}=\dfrac{6x-3}{2x(6x-3)}\\\\\boxed{(f/g)(x)=\dfrac{1}{2x}}\quad x\ne\dfrac{1}{2}[/tex]

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

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