Does y=1/x have an inverse? It is a one-to-one function, so it should be the inverse equation is the same???

yes, the inverse is the same.

Check it with G(f(x))

So, when drawing the inverse, it is just the same graph?

To determine whether the equation y = 1/x has an inverse, we need to establish whether it is a one-to-one function. A one-to-one function means that each input has a unique output. In this case, as x approaches positive or negative infinity, y approaches 0. Therefore, y = 1/x satisfies the criterion for a one-to-one function.

To find the inverse of the function y = 1/x, we can switch the places of x and y and solve for y. So, let's rewrite the function as x = 1/y.

To solve for y, we can multiply both sides of the equation by y and then divide both sides by x:

xy = 1
y = 1/x

As you can see, the inverse function is indeed the same as the original function, y = 1/x. This confirms that y = 1/x is its own inverse.

Now, let's talk about the graph of the inverse. Since the inverse equation is the same as the original equation, the graph of the inverse will be the same as the graph of y = 1/x. This means that if you were to graph both equations on a coordinate plane, they would overlap perfectly.