1.

`f(x)=log_(5)(cos^(-1)sqrt(x^(2)+5x+6)+sec^(-1)[{x}+1]([.]` denotes greatest integer function and `{.}` denotes fractional part function. Find the domain of `f(x)`:A. `[(-5-sqrt(5))/(2),-3]cup[-2,(-5+sqrt(5))/(2)]`B. `[(-sqrt(5)+5)/(2),-3]cup[-2,(5+sqrt(5))/(2))`C. `((-5+sqrt(5))/(4),-3]cup[-2,(-5+sqrt(5))/(4))`D. `((-5-sqrt(5))/(2),-3]cup[-2,(-5+sqrt(5))/(2))`

Answer» Correct Answer - D
Domain `sec^(-1)[{x}+1]` is R
`x^(2)+5x+6=0` at `x=-2,-3`
`x^(2)+5x+6=1atx=(-5sqrt(5))/(2).(-5sqrt(5))/(2)`
Domain of `f(x)` is `((-5-sqrt(5))/(2),-3]cup[-2,(-5+sqrt(5))/(2))`


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