Mark the correct alternative in each of the following: The inverse of the function f : R → [x ϵ R : x < 1] given by is The image displays the mathematical function f(x) = (e^x - e^(-x)) / (e^x + e^(-x)).

Q33 of 215 Page 3

Mark the correct alternative in each of the following:
The inverse of the function f : R → [x ϵ R : x < 1] given by is

Given that f: R → [x ϵ R : x < 1] defined by

Put y = f(x)

⇒ y(e^2x + 1)= e^2x – 1

⇒ e^2x (y -1) = -y -1

)

So, )

Mark the correct alternative in each of the following:

If f: R → R is given by f(x) = 3x – 5, then f^–1(x)

Mark the correct alternative in each of the following:

If g(f(x)) = |sin x| and f (g(x)) = , then

Mark the correct alternative in each of the following:

Let A = {x ϵR : x ≥ 1}. The inverse of the function f : A → A given by f(x) = 2^x(x–1), is

Mark the correct alternative in each of the following:

Let A = {x ϵ R: x ≤ 1} and f : A → A given by f(x) = x(2 – x).Then, f^–1(x) is