Plot two functions on the same plane, $y=f(x)$ and $x=g(y)$

Question

I'm trying to plot two functions. In general, this is not a difficult task, thanks e.g. to the command:

Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, PlotLabels -> "Expressions"]

However, I would like to plot two functions, one of them with respect to variable $x$ of the plane, and another with respect to the variable $y$. For example $y=\ln x$ and $x=y^2$.

Someone knows what should I do?

Answer 1

You can use ContourPlot, but then you have to supply the $y$-range:

ContourPlot[{y==Log[x], x == y^2}, {x, -2, 2}, {y, -2, 2}, Axes->True, Frame->False]

Answer 2

Both kinds of plots can be thought of as parametric plots, where for the first one $x$ is the independent parameter and for the second one $y$ is the independent parameter. With ParametricPlot take a parameter $t$ that is used in both roles:

f[x_] = Log[x];
g[y_] = y^2;
ParametricPlot[{{t, f[t]}, {g[t], t}}, {t, -1, 1}, 
  AspectRatio -> 1/GoldenRatio]