1.

Let a=sin^(-)(sin3)+sin^(-1)(sin4)+sin^(-1)(sin5),f(x)=e^(x^(2)+|x|), domain of f(x) be [a,oo) & range of f(x) be [b,oo) and g(x)=(4cos^(4)x-2cos2x-1/4"cos"4x-x^(7))^(1//7), domain & range of g(x) is set of real numbers. Which of the following are correct

Answer»

`a=-2`
`a+b=-1`
`F(G(g(b))=e^(2)`
Both `f(x), g(x)` are non invertible fns

Solution :`a=(pi-3)=(pi-4)+(5-2pi)=-2`
`f(-2)=f(2)impliesf(x)` is many one `IMPLIES` non invertible
Let `t=x^(2)+|x|,t epsilon [0,OO)`
`f(x) epsilon [1,oo)`
`impliesb=1` & `a+b=-1`
`g(x)=[(1+cos2x)^(2)-2cosx-1/2(2COS^(2)2x-1)-x^(7)]^(1//7)`
`g(x)=(3/2-x^(7)]^(1/7)`
`f(g(g(b)))=f(b)=e^(2)`


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