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  • What is the domain of the function f(x)=sin^-1 (log x^2) (where base is 4)

What is the domain of the function f(x)=sin^-1 (log x^2) (where base is 4)

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Solution:   We have , f(x)=sin^-1(log_4x^2)

     We know     ,   log_a^pm^n=fracnplog_am

        \ \ herefore hspace1cmlog_4x^2=log_2^2x^2=frac22log_2x=log_2x

                              f(x)    is defined , if x> 0

            \ \ Rightarrow hspace1cm -1leq log_2x leq 1\ \ Rightarrow hspace1cm2^-1leq x leq 2\ \ Rightarrow hspace1cmfrac12leq x leq 2

Hence Domain of     f(x)=[frac12,2]

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Deependra Verma

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