QuestionJune 24, 2025

Determine whether the equation y=3sqrt [7](x) defines y as a function of x. Does the equation y=3sqrt [7](x) define y as a function of x? A. No, because for any input x, the equation yields more than one output y. B. Yes, because any equation in terms of x and y is a function. C. No, because for any input x, the equation yields only one output y. D. Yes, because for any input x, the equation yields only one output y.

Determine whether the equation y=3sqrt [7](x) defines y as a function of x. Does the equation y=3sqrt [7](x) define y as a function of x? A. No, because for any input x, the equation yields more than one output y. B. Yes, because any equation in terms of x and y is a function. C. No, because for any input x, the equation yields only one output y. D. Yes, because for any input x, the equation yields only one output y.
Determine whether the equation y=3sqrt [7](x) defines y as a function of x.
Does the equation y=3sqrt [7](x) define y as a function of x?
A. No, because for any input x, the equation yields more than one output y.
B. Yes, because any equation in terms of x and y is a function.
C. No, because for any input x, the equation yields only one output y.
D. Yes, because for any input x, the equation yields only one output y.

Solution
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Answer

D. Yes, because for any input x, the equation yields only one output y. Explanation 1. Define a Function A function assigns exactly one output to each input. 2. Analyze the Equation For y = 3\sqrt[7]{x}, each input x gives exactly one output y. The seventh root is defined for all real numbers and provides a unique result. 3. Determine if it is a Function Since each x results in only one y, the equation defines y as a function of x.

Explanation

1. Define a Function<br /> A function assigns exactly one output to each input.<br />2. Analyze the Equation<br /> For $y = 3\sqrt[7]{x}$, each input $x$ gives exactly one output $y$. The seventh root is defined for all real numbers and provides a unique result.<br />3. Determine if it is a Function<br /> Since each $x$ results in only one $y$, the equation defines $y$ as a function of $x$.
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