Does a constant function have an inverse? Explain.?

Question

Does a constant function have an inverse? Explain.?

Answer 1

well yes and no. Because, a constant function has no arguments which really matter. Therefore, a constant function, say f(x)=3, is valid and holds at every x. Thus we say constant function is vacuously defined on an empty domain and consequently we do have an inverse, which you might have guessed happens to be the empty set itself,

I said no, because because an empty set really doesn't make a sense as an inverse.

Answer 2

A constant function does have an inverse, the problem is the inverse is not a function.

Just like when you solve for a f(x) = x²

y = x²

Swap x and y

x = y²

resolve for y

y = +/-√x

So the inverse of y=x² is y=+/-√x (which is not a function because it will fail the vertical line test.)

But what is really going on here, from a graphical stand point.

When you graph any function y = f(x) and generate it's inverse, the graphs are symmetrical about the line y=x

So take a function that is a constant like f(x) = 3

When you take the inverse... or look at the information that is symmetric about the line y=x, you'll see you generate a vertical line defined by x=3.

So yes, a constant function does have an inverse. It would be a vertical line (which is not a function).

Answer 3

No, there isn't. Please read through the source.