Is x2=4ay a function while y2=4ax is not?

Question

jchordig1d5 · Accepted Answer

This is typically written as f:X→Y.The symbol that stands for an arbitrary input, or the representing element of the domain, is called the independent variable. And similarly the dependent variable. It is a tradition to write x for the independent variable and y for the dependent variable.Now, first, let me assume a≠0. Otherwise you wouldn&#039;t have meaningful functions, but two equations. Also, I will assume that your domain and codomain are the set of real numbers. In your first exampley=x24a.Using this formula for each real numbered value of x, you can compute a value for y. Hence, by definition, we have a function.On the other hand, the second formula is y2=4ax,which produces a quadratic equation for y as soon as we assign a value for x. For example, lets set x=a, then y2=4a2 which has two solutions y=±2a. This isn&#039;t unique; hence doesn&#039;t agree with the definition of a function.Not only that, suppose a is positive, then for x=−1, we get y2=−4a which is impossible. This means that there is no value assigned to -1. One can restrict the domain and codomain to non-negative real values to remedy these two problems. Then even the second formula defines an honest function.

Is \(\displaystyle{x}^{{{2}}}={4}{a}{y}\) a function while \(\displaystyle{y}^{{{2}}}={4}{a}{x}\)

Answered question

Answer & Explanation

New Questions in Integral Calculus