The function g is defined by g x = x + 14 t - x , where t is a

Question

The function g is defined by g x = x + 14 t - x , where t is a constant. In the xy -plane, the graph of y = g x passes through the point 24 , 0 . What is the value of g 0 ?

Accepted Answer

The correct answer is 336 . By the zero product property, if x + 14 t - x = 0 , then x + 14 = 0 , which gives x = - 14 , or t - x = 0 , which gives x = t . Therefore, g x = 0 when x = - 14 and when x = t . Since the graph of y = g x passes through the point 24 , 0 , it follows that g 24 = 0 , so t = 24 . Substituting 24 for t in the equation g x = x + 14 t - x yields g x = x + 14 24 - x . The value of g 0 can be calculated by substituting 0 for x in this equation, which yields g 0 = 0 + 14 24 - 0 , or g 0 = 336 .

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