The function f is defined by f(x) = 8√x. For what value of x does f(x) = 48? | SAT Polynomial and other nonlinear functions Practice

Choice C is correct. It's given that $f(x) = 8\sqrt{x}$ . Substituting $48$ for $f(x)$ in this equation yields $48 = 8\sqrt{x}$ . Dividing both sides of this equation by $8$ yields $6 = \sqrt{x}$ . This can be rewritten as $\sqrt{x} = 6$ . Squaring both sides of this equation yields $x = 36$ . Therefore, the value of $x$ for which $f(x) = 48$ is $36$ .

Choice A is incorrect If $x = 6$ , $f(x) = 8\sqrt{6}$ , not $48$ .

Choice B is incorrect. If $x = 8$ , $f(x) = 8\sqrt{8}$ , not $48$ .

Choice D is incorrect. If $x = 64$ , $f(x) = 8\sqrt{64}$ , which is equivalent to $64$ , not $48$ .

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