The domain of the function f(x)=sin^-1 (2x^2+3x+1) , is

Answers (1)

Solution:     We have ,    f(x)=sin^-1(2x^2+3x+1)

                 Rightarrow       -1leq(2x^2+3x+1)leq1,

                 Rightarrow       -frac12leq(x+frac34)^2leq frac916,

                Rightarrow         (x+frac34)^2leq frac916

               Rightarrow          -frac34leq (x+frac34)leq frac34

              Rightarrow           -frac32leq x< 0      Rightarrow       D(f)=(-frac32,0] .

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