Interpreting Mathematica output or producing cleaner output [closed]

Could someone please explain what the following would look like in standard math notation (or explain to me what this means):

InverseFunction[(
z Log[1 - #1] + (1 - 2 z) Log[#1] + (-1 + z) Log[z - #1 + z #1])/(
z (-1 + 2 z)) &][-(t/2) + (
z Log[1 - a0] + Log[a0] - 2 z Log[a0] - Log[z - a0 + z a0] +
z Log[z - a0 + z a0])/(z (-1 + 2 z))]


I'm new to Mathematica so the use of the pure functions is a little confusing, especially since it's been combined with the inverse.

Also is there a way to get Mathematica to print this without using pure functions?

• "Also is there a way to get Mathematica to print this without using pure functions?" - not really. To interpret something like InverseFunction[Tan[#] &][x], it just says it is the inverse function of Tan[] applied to its argument x; that is, ArcTan[]. Since most functions do not admit an easy representation for the inverse, we sometimes cannot avoid InverseFunction[]. – J. M. is in limbo May 2 '15 at 15:39
• @J.M. that;s a valid answer from my point of view :) – Kuba Dec 7 '15 at 13:55

One way to write it is to let $$f(x) = \frac{z \log (1-x)+(1-2 z) \log (x)+(z-1) \log (x z-x+z)}{z (2 z-1)}$$ and write $f^{(-1)}\left(\frac{z \log (1-{a_0})-2 z \log ({a_0})+z \log ({a_0} z-{a_0}+z)-\log ({a_0} z-{a_0}+z)+\log ({a_0})}{z (2 z-1)}-\frac{t}{2}\right)$ for InverseFunction[..][..]. So in regular mathematical notation, the expression is done in two pieces (or sometimes more). In Mathematica, one needs a single expression (to compute with). I doubt there's a simpler way than InverseFunction[..][..].