Which of the follo wing is/are true? `f(x)=e^x and g(x)=Inx`, then `f(g(x)) = x` (wherever `f(g(x))` is defined)

Let f(x) = sqrt(2-x-x^(2)) and g(x) = cos x . Which of the following statement are true ? (I) Domain of f((f(x))^(2)) = Domain of f(g(x)) (II) Domain of f(g(x)) + g(f(x)) = Domain of f(g(x)) (III) Domain of f(g(x)) = Domain of f(g(x)) (IV) Domain of g((f(x))^(3)) = Domain of f(g(x))

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? [f(x)]^(g(x)) is always increasing [f(x)]^(g(x)) is decreasing, when f(x) 1. If f(x)>1,t h e n[f(x)]^(g(x)) is increasing.

If f(x) and g(x) are two positive and increasing functions,then which of the following is not always true? [f(x)]^(g(x)) is always increasing [f(x)]^(g(x)) is decreasing, when f(x) 1. If f(x)>1, then [f(x)]^(g(x)) is increasing.

If f:RtoR and g:RtoR defined by f(x)=x^2 and g(x)=x+1 , then gof(x) is

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

If f(x)=log_ex and g(x)=e^x , prove that f{g(x)}=g{f(x)} .

Function f and g defined on R-{0}rarrR as f(x)=x and g(x)=1/x" then "f.g(x) = ...... .

If f(x)=e^(x) and g(x)=f(x)+f^(-1) , what does g(2) equal?