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Advanced Math / Nonlinear functions Difficulty: Hard

fx=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 ?

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Explanation

Choice B is correct. It’s given that fx=94x and gx=fx+2. Substituting x+2 for x in fx=94x gives fx+2=94x+2. Rewriting this equation using properties of exponents gives fx+2=94x42, which is equivalent to fx+2=94x16. Multiplying 9 and 16 in this equation gives fx+2=1444x. Since gx=fx+2, gx=1444x.

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.