I would like to find the root of the following function:
x=0.5 f <- function(y) ((1-pbeta(1-exp(-0.002926543 *( 107.2592+y)^1.082618
Try using a small interval but allow uniroot() to extend the interval:
uniroot(f, lower=0, upper=1, extendInt = "yes")$root [1] -102.9519