Question

Write the equation \(16x - y^4 = 0\) as a function for \(y\).**

A. \(y = \sqrt[4]{16x}\)
B. \(y = -\sqrt[4]{16x}\)
C. \(y = 2x\)
D. \(y = -2x\)

Answer 1

The equation 16x - y⁴ = 0 as a function for y =
`\sqrt[4]{16x}\)`. Thus, the correct answer is A. y =
`\sqrt[4]{16x}\)`

Step-by-step explanation:

The given equation is 16x - y⁴ = 0. To express y as a function of x, we need to isolate y on one side of the equation. Starting with the given equation:

16x - y⁴ = 0

Add y⁴ to both sides:

16x = y⁴

To solve for y, take the fourth root of both sides:

y =
`\sqrt[4]{16x}`

So, the correct expression for y as a function of x is y =
`\sqrt[4]{16x}\)`, which corresponds to option A.

In this expression, y is the fourth root of 16x, representing a positive value. The fourth root ensures that both positive and negative solutions are considered, but the positive root is selected to match the traditional representation of functions.

Therefore, option A, y =
`\sqrt[4]{16x}\)`, accurately represents the given equation as a function of y in terms of x.