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 ...

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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

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onto but not one-one

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Both one-one and onto

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neither one-one nor onto

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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.

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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.