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Show that the function f : R ->R, define...

Show that the function `f : R ->R`, defined as `f(x)=x^2`, is neither one-one nor onto.

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Given: `f:R→R:f(x)=x^2`
`f(x)=x^2`
For, `f(x_1)=f(x_2)`
`=>(x^2)_1=(x^2)_2`
`=>x_1=x_2`
Since `x_1` doesn’t has unique image
`therefore``f(x)` is not one-one
...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
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  2. Prove that f: R->R , given by f(x)=2x , is one-one and onto.

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  3. Show that the function f : R ->R, defined as f(x)=x^2, is neither one-...

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  4. Show that f: R->R , defined as f(x)=x^3 , is a bijection.

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  14. Let f: N-{1}->N be defined by, f(n)= the highest prime factor of n ...

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  15. Let A={1,2} . Find all one-to-one function from A to A.

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  19. Show that the function f: R->R given by f(x)=x^3+x is a bijection.

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  20. Show that f:n->N defined by f(n)={(((n+1)/2,(if n is odd)),(n/2,(if n ...

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