Find domain of sin^-1(√(x^2)-1) - Maths - Inverse Trigonometric Functions

Question

Find domain of sin^-1(√(x^2)-1)

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

y=sin-1x2-1As, the domain of sin-1x=-1,1 i
e
 -1≤x≤1So, the domain of sin-1x2-1 is given by-1≤x2-1≤1⇒0≤x2-1≤1⇒1≤x2≤2⇒x2≥1 and x2≤2⇒x2-1≥0 and x2-2≤0⇒x2-12≥0 and x2-22≤0⇒x+1x-1≥0 and x+2x-2≤0⇒x∈(-∞,-1]∪[1,∞) and x∈-2,2⇒x∈-2,-1∪1,2Hence, the domain of the given function is

Hope
this
information will clear
your doubts about the
topic
Regards

Find domain of sin^-1(√(x^2)-1).