Question

Determine whether the equation represents y as a function of x 16x-y^4=0

Answer 1

Given

`16x-y^4=0 \\ \\ \Rightarrow y^4=16x \\ \\ \Rightarrow y= \sqrt[4]{16x} =2 \sqrt[4]{x}`

For any value of x, there are two possible values of y, thus the equation does not represent y as a function of x.

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.