Given
[tex]16x-y^4=0 \\ \\ \Rightarrow y^4=16x \\ \\ \Rightarrow y= \sqrt[4]{16x} =2 \sqrt[4]{x} [/tex]
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.
