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If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain of (f*g)(x)?

User Mmackh
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(f.g)(x) =( f(x))(g(x)) \\ = ( {x}^(2) - 1)(2x - 3) \\ = (x - 1)(x + 1)(2x - 3)
then the domain of (f•g)(x) is {-1, 1, 3/2}
User Paul Farnell
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2 votes

Answer:

domain is the set of all real values for x (-∞,∞)

Explanation:


f(x) = x^2 -1 and
g(x) = 2x - 3

We need to find the domain of
(f \cdot g)


(f \cdot g)=f(x) \cdot g(x)

Plug in f(x) and g(x)


(f \cdot g)=(x^2 -1)(2x-3)

Multiply it using FOIL method


(x^2 -1)(2x-3)


f(x) \cdot g(x)=(2x^3-3x^2-2x+3)

WE got an cubic equation, there is no restriction for x.

So domain is the set of all real values for x (-∞,∞)

User Carlos Cervantes
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