Let's say x = 1000, shape=2, scale=1500.
Then y=pweibull(x=1000, shape = 2, scale = 1500) produces y=0.3588196.
I need to find x, given (y, shape, scale).
However, none of pinvweibull, qinvweibull, levinvweibull, etc. is giving me x.
How can I find the x for which I have y=pweibull(x=1000, shape = 2, scale = 1500) ?
You're looking for qweibull which is the inverse cdf:
qweibull(0.3588196, 2, 1500)
[1] 1000
Check the documentation with ?qweibull. You'll see four functions d*, p*, q*, and r* for density, cdf, inverse cdf, and random variates. This is pretty standard for distributions in R (see e.g. ?dnorm or ?dbeta).