Let `g:R rarr R` be defined as `g(x)=(e^(x)-e^(-x))/(2)` If `g(f(x))=x` ,then the value of `f((e^(100)-1)/(2e^(50)))`

Let f:R rarr R" be defined by "f(x)=(e^(|x|)-e^(-x))/(e^(x)+e^(-x)). Then

Let f:R rarr R defined by f(x)=x^(3)+e^(x/2) and let g(x)=f^(-1)(x) then the value of g'(1) is

Let f:R rarr R defined by f(x)=x^(3)+e^((x/2)) and let g(x)=f^(-1)(x) then the value of g'(1) is

Let f(x) = (e^(x) - e^(-x))/(2) and if g(f(x)) = x , then g((e^(1002) -1)/(2e^(501))) equals ...........

Let g:R rarr R be defined as g(x)=(x^(3)+e^(2x)-1)/(2). If g(f(x))=x while f((e^(4)+7)/(2))=alpha ,then find the number of solution(s) of the equation |x-2|-3|-alpha=0

(ii) Let g:R rarr R be defined as g(x)=(x^(3)+e^(2x)-1)/(2) . If g(f(x))=x while f((e^(4)+7)/(2))=alpha ,then find the number of solution(s) of the equation ||x-2|-3|-alpha=0

Let f:R rarr R be a function defined by,f(x)=(e^(|x|)-e^(-x))/(e^(x)+e^(-x)) then

Let f:R rarr R, be defined as f(x)=e^(x^(2))+cos x, then f is a

R rarr R be defined by f(x)=((e^(2x)-e^(-2x)))/(2) is f(x) invertible.If yes then find f^(-1)(x)