g x = 3 5 x + 7 6 h x = 6 x - 5 The functions g and

Question

g x = 3 5 x + 7 6 h x = 6 x - 5 The functions g and h are defined by the equations shown. Which expression is equivalent to g x &#183; h x ?

Accepted Answer

Choice D is correct. It&rsquo;s given that g x = 3 5 x + 7 6 and h x = 6 x - 5 . Substituting 3 5 x + 7 6 for g x and 6 x - 5 for h x in the expression g x &#183; h x yields 3 5 x + 7 6 6 x - 5 . This expression can be rewritten as 3 5 x 6 x - 5 + 7 6 6 x - 5 , or 18 x 2 5 - 3 x + 7 x - 35 6 , which is equivalent to 18 x 2 5 + 4 x - 35 6 . Choice A is incorrect. This expression is equivalent to 3 5 x 6 x + 7 6 - 5 , not 3 5 x + 7 6 6 x - 5 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This expression is equivalent to 3 5 x - 7 6 6 x + 5 , not 3 5 x + 7 6 6 x - 5 .

Question g-x-3-