f x = 9 ( 4 ) x The function f is defined by the given equation. If g (

Question

f x = 9 ( 4 ) x The function f is defined by the given equation. If g ( x ) = f ( x + 2 ) , which of the following equations defines the function g ?

Accepted Answer

Choice B is correct. It&rsquo;s given that f x = 9 4 x and g x = f x + 2 . Substituting x + 2 for x in f x = 9 4 x gives f x + 2 = 9 4 x + 2 . Rewriting this equation using properties of exponents gives f x + 2 = 9 4 x 4 2 , which is equivalent to f x + 2 = 9 4 x 16 . Multiplying 9 and 16 in this equation gives f x + 2 = 144 4 x . Since g x = f x + 2 , g x = 144 4 x . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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