Grade 12Algebra

The function f : ¡ to ¡ defined by f (x)= x |x| will be
A. many-to-one and onto
B. one-to-one and onto
C. many-to-one and into
D. one-to-one and into

Anirudh D Menon

8 Years agoGrade 12

4 Answers

Amit

Approved Tutor Answer8 Years ago

Hi there. You can just draw graph and analyse .. For ex. For x0 f(x) will be x². Now try to plot it. It would something of x³ type..graph. Hence it is one one and onto.

Amit

8 Years ago

For x>0 it will be x² and for x

Samyak Jain

8 Years ago

f : R $\rightarrow$ R ; f(x) = x |x|

For x > 0, f(x) = x.x = x².

For x = 0, f(x) = 0 .

For x ²

$\therefore$ The graph of f(x) is always increasing from – infinity to + infinity.

So it is one-one.

Moreover, f(x) covers all the elements of the set of real numbers.

So it is onto.

$\therefore$ f(x) = x |x| is one-one and onto function.

Samyak Jain

8 Years ago

f : R $\rightarrow$ R ; f(x) = x |x|

For x > 0, f(x) = x.x = x².

For x = 0, f(x) = 0 .

For x ².

$\therefore$ The graph of f(x) is always increasing from – infinity to + infinity.

So it is one-one.

Moreover, f(x) covers all the elements of the set of real numbers.

So it is onto.

$\therefore$ f(x) = x |x| is one-one and onto function.

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View all Questions

The function f : ¡ to ¡ defined by f (x)= x |x| will beA. many-to-one and ontoB. one-to-one and ontoC. many-to-one and intoD. one-to-one and into

Anirudh D Menon

4 Answers

Amit

Amit

Samyak Jain

Samyak Jain

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The function f : ¡ to ¡ defined by f (x)= x |x| will be
A. many-to-one and onto
B. one-to-one and onto
C. many-to-one and into
D. one-to-one and into