Graphing an inverse parametrically

Question

My calculus book has the following question:

Graph the one - to - one function $ f(x) = x^2$ , where x is greater than or equal to zero, with its inverse.

Now my answer is that the inverse is the graph of: $ y = \sqrt { x }$ .

The book says that the answer is the graph of: $x = t^2$ , $y = t$ , where t is more than or equal to 0.

How did they get this answer? Thanks!

Answer 1

It is easy. For all $(x_1,x_2)=(x_1,f(x_1))$ the inverse function should give $(x_2,x_1)$. Namely you will just the change of the place of $y$ and $x$ in the original equation. In other words take the square of the equation that you have already found.

Answer 2

Now consider $x=t^2 $ as You're Domain, And $y=\sqrt{x}=\sqrt {t ^ 2}=t $ As You're Range