If A - -1- 1- and f - A- Ais defined as f x - x-x- for all xbelongs to A- then fx is

Explanation for correct option:Finding type of relation.Given that A = [ 1, 1] and f : A→ Ais define as f (x) = x|x|,∀ x ∈ Af(x) = x^2 for x > 0 and f (x) = ...

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

Byju's Answer

Standard XII

Mathematics

Inverse of a Function

If A = [-1, 1...

Question

If $A = [- 1, 1] a n d f : A \to A$ is defined as $f (x) = x | x |,$ for all $x$ belongs to $A,$ then $f (x)$ is

$m a n y - o n e a n d i n t o f u n c t i o n$

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

$o n e - o n e a n d i n t o f u n c t i o n$

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

$m a n y - o n e a n d o n t o f u n c t i o n$

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

$o n e - o n e a n d o n t o f u n c t i o n$

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

Open in App

Solution

The correct option is D
$o n e - o n e a n d o n t o f u n c t i o n$

Explanation for correct option:
Finding type of relation.
Given that $A = [- 1, 1] a n d f : A \to A$ is define as $f (x) = x | x |, \forall x \in A$
$f (x) = x^{2} f o r x > 0 a n d f (x) = - x^{2} f o r x < 0$
$f (x) = x^{2}$ ranges from $0 t o 1$ , when $x$ ranges from ranges from $0 t o 1$ , also $f (x) = - x^{2}$ ranges from $0 t o - 1$ , when x ranges from $0 t o - 1$ .
The function is one-one and onto.
Hence, correct option is $d$

Suggest Corrections

Similar questions

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

Q. Let

A = [- 1, 1]

and

f : A \to A

be defined as

f (x) = x | x |

for all

x \in A

, then

f (x)

Q. If f (x) is defined on [0,1] as f (x)={x if x belongs to Q and 1-x if x does not belongs to Q } where f( f (x) )=

If f:R--> R be a function given by

f(x+y) = f(x) f(y) for all x,y belongs to R.
Prove that f(x) = [f(1)]^x for all x belongs to R.

Q. IF f:R to R be defined as follows:
F(x)= {1, if x belongs to Q}
F(x)={-1,if x does not belongs to Q}
find
1)f(1/2),f(pi), f(root 2)
2)range of f
3)pre images of 1 and -1

Join BYJU'S Learning Program

If A=[-1,1]andf:A→Ais defined as f(x)=x|x|, for all xbelongs to A, then f(x) is

If $A = [- 1, 1] a n d f : A \to A$ is defined as $f (x) = x | x |,$ for all $x$ belongs to $A,$ then $f (x)$ is