y = sine inverse of 2/ x+1 find the non-differentiability points in domain

Question

y = sine  inverse of 2 / x+1

Answer 1

If this is y=sin⁻¹(2/(x+1)), then sin(y)=2/(x+1).

Since -1≤sin(y)≤1, this puts constraints on x, the domain. 2/(x+1)≥-1 and 2/(x+1)≤1.

From these, x≤-3 and x≥1, and so the function is undifferentiable when -3<x<1. Note that x=-1 is within this prohibited interval, so we don’t need to isolate the case when 2/(x+1) is undefined.