Example OW.ICPPF.3 : $InvP_4(x)=+\sqrt[4] x$.
Draw a mapping diagram and graph of $InvP_4$ yourself, or consider the GeoGebra figures and table below.

Martin Flashman, Nov. 9, 2013, Created with GeoGebra

The  GeoGebra figure illustrates the key property for an inverse: $(P_4^{-1} \circ P_4 )(x) =x$ for all $x \in [0,\infty)$
Notice how the points on the graph are paired with the points on the mapping diagram.
Given a point / number, $x$, on the source line, there is a unique arrow  meeting the first target line at the point / number, $P_4(x)=x^4$, and  another arrow from the first target line to the point on the second target line  $P_4^{-1} (P_4(x))=+\sqrt[4] {x^4} = x$. which corresponds to the inverse core function's value for $P_4(x)$.
Check the box in GeoGebra to see more points and arrows corresponding to data on the table.
When the point in the domain is $0$, the arrow points to $P_4^{-1} (0) = 0$ visualizing the "Y-intercept" on the graph of $P_4^{-1}$.
This is the unique X- intercept as well.
The function is  increasing for all $x \in (0,\infty)$.
You can check this by moving $x$ on the GeoGebra mapping diagram.