I would like to get x from the following function when the y is known and which + means If $1$ is bigger than x its equal $ 1 - x$ and else it's equal zero. Also, + means If x is bigger than 5 its equal $x-5$ and else it's equal zero:
$$ 0.1 x + (\frac{1}{2} - \frac{(1-x)_{+}^2}{2}) + (\frac{(x-5)^{2}_{+}}{2}) = -\log(1-y)$$
Write the left side as $$f(x)=\begin {cases} \frac 12(\frac x5+2x-x^2)&x \lt 1\\ \frac x{10}+\frac 12&1 \le x \lt 5\\ \frac 12(x^2-9.8x+26)&x \ge 5 \end {cases}$$ Given the right side, you can solve each of these and see if $x$ is in the correct range.