f x = 272 2 x The function f is defined by the given equation. If h x = f

Question

f x = 272 2 x The function f is defined by the given equation. If h x = f x - 4 , which of the following equations defines function h ?

Accepted Answer

Choice A is correct. It's given that f ( x ) = 272 ( 2 ) x and h ( x ) = f ( x - 4 ) . Substituting x - 4 for x in f ( x ) = 272 ( 2 ) x yields f x - 4 = 272 2 x - 4 . Substituting h x for f x - 4 in this equation yields h x = 272 2 x - 4 . Using the properties of exponents, the function h ( x ) = 272 ( 2 ) x - 4 can be rewritten as h x = 272 2 x 2 4 , which is equivalent to h x = 272 2 x 16 , or h ( x ) = 17 ( 2 ) x . Therefore, of the given choices, an equation that defines function h is h ( x ) = 17 ( 2 ) x . Choice B is incorrect. This equation defines function h if h ( x ) = f ( x - 2 ) , not h ( x ) = f ( x - 4 ) . Choice C is incorrect. This equation defines function h if h ( x ) = f ( 4 x ) , not h ( x ) = f ( x - 4 ) . Choice D is incorrect and may result from conceptual or calculation errors.

Question f-x-27