Mark the correct alternative in each of the following: Let Then, for what value of α is f(f(x)) = x? The image displays the mathematical function f(x) = (αx) / (x + 1), with the condition x is not equal to -1.

Given that , x≠-1 and f(f(x)) = x⇒ α2x = x(αx + x + 1)⇒ α2 = αx + x + 1⇒ α2 - αx = x + 1On comparing - αx with x,We get α = -1

Q40 of 215 Page 3

Mark the correct alternative in each of the following:
Let Then, for what value of α is f(f(x)) = x?

Given that , x≠-1 and f(f(x)) = x

⇒ α²x = x(αx + x + 1)

⇒ α² = αx + x + 1

⇒ α² - αx = x + 1

On comparing - αx with x,

We get α = -1

Mark the correct alternative in each of the following:

If F: [1, ∞) → [2, ∞) is given by then f^–1(x) equals.

Mark the correct alternative in each of the following:

Let g(x) = 1 + x – [x] and where [x] denotes the greatest integer less than or equal to x. Then for all x, f (g(x)) is equal to

Mark the correct alternative in each of the following:

The distinct linear functions which map [–1, 1] onto [0, 2] are

Mark the correct alternative in each of the following:

Let f : [2, ∞) → X be defined by f(x) = 4x – x². Then, f is invertible, if X =