Let f x be a function defined on -0-1- such that f x -left begin matrix x- - if - X -epsilon - Q -1-x- if - X - hot epsilon - Q -Then- for all x -0-1- ffx-A- constantB- 1- xC- none of theseD- X

The correct option is D x If x ϵ Q, f(x)=x f{f(x)}=f(x)=x If x ϵ̸ Q, f(x)=1 x f{f(x)}= f(1 x) = 1 (1 x) = x ⇒ f{f(x)} = x ∀ x ϵ [0,1] ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Definition of Functions

Let f x be a ...

Question

Let f(x) be a function defined on [0, 1] such that $f (x) = {\begin{matrix} x, & i f x ϵ Q 1 - x, & i f x / ϵ Q \end{matrix}$
Then, for all $x ϵ [0, 1], f (f (x)) =$

constant

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$1 + x$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$x$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$x$

$I f x ϵ Q, f (x) = x f {f (x)} = f (x) = x I f x / ϵ Q, f (x) = 1 - x f {f (x)} = f (1 - x) = 1 - (1 - x) = x \Rightarrow f {f (x)} = x \forall x ϵ [0, 1]$

Suggest Corrections

Similar questions

Q. Let f(x) be a function defined on [0, 1] such that

f (x) = {\begin{matrix} x, & i f x ϵ Q 1 - x, & i f x / ϵ Q \end{matrix}

Then, for all

x ϵ [0, 1], f (f (x)) =

Let f(x) be a function defined on [0, 1] such that $f (x) = {\begin{matrix} x, & i f x ϵ Q 1 - x, & i f x / ϵ Q \end{matrix}$
Then, for all $x ϵ [0, 1], f (f (x)) =$

Q. If

f (x)

is defined on

[0, 1]

by the rule

f (x) = {\begin{matrix} x & , & i f & x \in Q 1 - x & , & i f & x \notin Q \end{matrix}

Then, for all

x \in [0, 1]

prove that

f (f (x)) = x

Q. Let f defined on [0, 1] be twice differentiable such that | f"(x) | ≤ 1 for all x ∈ [0, 1]. If f(0) = f(1), then show that | f'(x) | < 1 for all x ∈ [ 0, 1].

Join BYJU'S Learning Program

Let f(x) be a function defined on [0, 1] such that f(x)={x, if x ϵ Q1−x, if x /ϵ Q Then, for all x ϵ [0,1],f(f(x))=

The correct option is C x If x ϵ Q,f(x)=xf{f(x)}=f(x)=xIf x /ϵ Q,f(x)=1−xf{f(x)}=f(1−x)=1−(1−x)=x⇒f{f(x)}=x ∀ x ϵ [0,1]

Let f(x) be a function defined on [0, 1] such that $f (x) = {\begin{matrix} x, & i f x ϵ Q 1 - x, & i f x / ϵ Q \end{matrix}$
Then, for all $x ϵ [0, 1], f (f (x)) =$

The correct option is C
$x$

$I f x ϵ Q, f (x) = x f {f (x)} = f (x) = x I f x / ϵ Q, f (x) = 1 - x f {f (x)} = f (1 - x) = 1 - (1 - x) = x \Rightarrow f {f (x)} = x \forall x ϵ [0, 1]$