solve for y: $x = 1 - (1-y)^t$

Question

I have the following equation:

$$x = 1 - (1-y)^t$$

I would like to solve for $y$ in terms of $x$ and $t$. I tried WolframAlpha, but it did not generate a solution. Before you ask, yes this is a real problem, no this is not homework.

Answer 1

$$x = 1 - (1-y)^t$$ $$(1-y)^t=1-x$$ Notice that the following step does not always hold, for example if $t=2$, and $x>1$, we end up with no solution for $y$. But suppose every value is proper, we then have: $$\bigg( (1-y)^t \bigg)^{1/t}=(1-x)^{1/t}$$ $$1-y=(1-x)^{1/t}$$ $$-y=(1-x)^{1/t} -1$$ $$y=1-(1-x)^{1/t}$$