OG详解-OG6 数学2 Q24

Choice D is correct. It’s given that f(24)<0. Substituting 24 for f(x) in the equation f(x) = a√x+b​ yields f(24) = a√24​+b. Therefore, a√24​+b< 0. Since √24​+b can’t be negative, it follows that a < 0. It’s also given that the graph of y = f(x) passes through the point (-24, 0). It follows that when x =-24, f(x) = 0. Substituting -24 for x and 0 for f(x) in the equation f(x) = a√x​+byields 0 = a √−24+b​. By the zero product property, either a = 0 or  √−24+b​= 0. Since a <0, it follows that√24+b​= 0. Squaring both sides of this equation yields -24+b = 0. Adding 24 to both sides of this equation yields b = 24. Since a <0 and b is 24, it follows that a<b must be true.
Choice A is incorrect. The value of f(0) is a√​b, which must be negative. Choice B  is incorrect. The value of f(0) is a√​b, which could be -24, but doesn’t have to be. Choice C is incorrect and may result from conceptual or calculation errors.