Find $Y=f(X)$ such that $Y \sim \text{Uniform}(-1,1)$. 
If $X_1,X_2\sim \text{Normal} (0,1)$, then find $Y=f(X)$ such that $Y \sim \text{Uniform}(-1,1)$.

I solve problems where transformation is given and I need to find the distribution. But here I need to find the transformation. I have  no idea how to proceed. Please help.

The cumulative distribution function $F(X)$ for any random variable $X$ always have a $U(0,1)$ distribution. Hence, $2F(X)-1$ will always follow $U(-1,1)$ distribution.
Regards
Nicola Bradshaw
http://tutorteddy.com/site/free_statistics_help.php
