F - R - R - f x - x - x - isA- one-one but not ontoB- onto but not one-oneC- Both one-one and ontoD- neither one-one nor onto

The correct option is C Both one one and onto Give that f(x){ x^2 if x gt;0 0 if x=0 x^2 if x lt;0 . draw the graph , and you'll see that f is one on ...

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

Byju's Answer

Standard XII

Mathematics

Bijective Function

f : R → R , f...

Question

$f : R \to R, f (x) = x | x | i s$

one-one but not onto

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

onto but not one-one

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

Both one-one and onto

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

neither one-one nor onto

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

Open in App

Solution

The correct option is C
Both one-one and onto

$G i v e t h a t f (x) ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x^{2} i f x > 0 0 i f x = 0 - x^{2} i f x < 0 \end{matrix}$
draw the graph , and you'll see that f is one-one and onto.

Suggest Corrections

Similar questions

Q. The function

f : R \to R

defined by

f (x) = (x - 1) (x - 2) (x - 3)

is
(a) one-one but not onto
(b) onto but not one-one
(c) both one and onto
(d) neither one-one nor onto

Q. The function f : R

\to

Rdefined by f(x) =(x - 1)(x - 2)(x - 3) is

Q. The function

f : R \to R

defined by

f (x) = x^{3} + 2

The function f:[0, 3]→[1,29], defined by f(x)=2x³-15x²+36x+1, is

Q. The function f : R

\to

Rdefined by f(x) =(x - 1)(x - 2)(x - 3) is

Join BYJU'S Learning Program

f:R→R, f(x)=x|x| is

The correct option is C Both one-one and onto Give that f(x)⎧⎪⎨⎪⎩x2 if x>00 if x=0−x2 if x<0 draw the graph , and you'll see that f is one-one and onto.

$f : R \to R, f (x) = x | x | i s$

The correct option is C
Both one-one and onto

$G i v e t h a t f (x) ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x^{2} i f x > 0 0 i f x = 0 - x^{2} i f x < 0 \end{matrix}$
draw the graph , and you'll see that f is one-one and onto.