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Nonlinear functions SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

The function $p$ is defined by $p (n) = 7 n^{3}$ . What is the value of $n$ when $p (n)$ is equal to $56$ ?

ExplanationShow

Choice A is correct. It's given that $p (n) = 7 n^{3}$ . Substituting $56$ for $p (n)$ in this equation yields $56 = 7 n^{3}$ . Dividing each side of this equation by $7$ yields $8 = n^{3}$ . Taking the cube root of each side of this equation yields $2 = n$ . Therefore, when $p (n)$ is equal to $56$ , the value of $n$ is $2$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

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