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A={x:-1 le x le 1}, f: A to A defined by...

`A={x:-1 le x le 1}, f: A to A` defined by `f(x) =x|x|`. Then f is:

A

a bijection

B

an injection but not surjection

C

a surjection but not an injection

D

neither an injection nor a surjection

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The correct Answer is:
A
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
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  2. If f: R to R is defined by f(x) =x+ sqrt(x^(2)), then f is:

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  3. A={x:-1 le x le 1}, f: A to A defined by f(x) =x|x|. Then f is:

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  4. If f(x)=|x-1|+|x-2|+|x-3|,2 lt x lt 3, then f is

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  5. y=f(x) =x/(1+|x|), x in R, y in R is

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  6. f: R to R is a function defined by f(x) =(e^(|x|) -e^(-x))/(e^(x) + e^...

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  7. If f: R to R defined by f(x) =(e^(x^(2)) -e^(-x^(2)))/(e^(x^(2)) +e^(-...

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  8. If f:[0,1] to [-1,3] defined by f(x) =x^(2)+x+1, then f is

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  9. If f: R to R defined by f(x) =x^(2)-2x-3, then f is:

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  10. If f:R rarr(0, 1] is defined by f(x)=(1)/(x^(2)+1), then f is

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  11. If f: R to R is defined by f(x)=(x^(2)-4)/(x^(2)+1), then f(x) is

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  12. Which of the following functions is not injective ?

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  13. The function f: R to R defined by f(x) =x-[x], AA x in R is

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  14. f: R^(+) to R defined by f(x) =2^(x) , x in (0,1), f(x) =3^(x), x in [...

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  15. f: R^(+) to R defined by f(x) = log(e)x, x in (0,1), f(x) =2 log(e) x,...

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  16. Statement -I: f: A to B is one -one and g: B to C is a one-one functio...

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  17. Observe the following Lists: Then the match for List -1 from Lis...

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  18. If f(x) =(e^(x) + e^(-x))/2, then the inverse function of f(x) is:

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  19. If f(x) =(10^(x)-10^(-x))/(10^(x) +10^(-x)) then f^(-1)(x)=

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  20. Let f: [1/2, 1] to [-1,1] is given by f(x) =4x^(3)-3x and f^(-)(x) is ...

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