Is this equation a function?Why/Why not?

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1 Answer
Aug 2, 2016

x=(y-2)^2+3 is an equation with two variables and hence we can express it both as x=f(y) as well as y=f(x). Solving for y we get y=sqrt(x-3)+2

Explanation:

Just as in case of f(x)=(x-2)^2+3, f is a function of x and when we try to draw such a function on say Cartesian coordinates, we use y=f(x). But x and y are just two variables and nature of function does not change, when we replace x by y and y by x.

However, a Cartesian graph of the function does change. This is as we always consider x as horizontal axis and y as vertical axis. We do not reverse these axes, but why we do not do that, because everybody understands that way and no body wants any confusion.

Similarly, in x=(y-2)^2+3 we have x as a function of y which can be written as x=f(y).

Further x=(y-2)^2+3 is an equation with two variables and hence we can express it both as x=f(y) as well as y=f(x). In fact solving for y we get y=sqrt(x-3)+2

However, there is a limitation as in x=f(y), we find there is an x for all values of y, but in y=f(x), y is not defined for x<3.