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Let f:R-R be defined as f(x) = x^4, then...

Let `f:R-R` be defined as `f(x) = x^4`, then (a) f is one-one (b) f is many-one onto (c) f is one-one but not onto (d) f is neither one-one nor onto

A

f is one-one

B

f is many-one onto

C

f is one-one but not onto

D

f is neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
D
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BETTER CHOICE PUBLICATION-RELATIONS AND FUNCTIONS -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

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  2. Give an example of a relation which is symmetric and transitive but no...

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  3. Let f(x) = [x] and g(x) = |x| then find the value of (fog)(1/2) - ...

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  4. Let f(x) = [x] and g(x) = |x| then find the value of (gof) (5/3) -...

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  5. If f, g: Rrarr R are defined by f(x) = x^2 + 3x+1,g(x) = 2x – 3 then f...

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  6. If f, g: Rrarr R are defined by f(x) = x^2 + 3x+1,g(x) = 2x – 3 then f...

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  7. If f, g : R rarr R are defined respectively by : f (x) = x^2 + 3x + 1 ...

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  8. If f, g : R rarr R are defined respectively by : f (x) = x^2 + 3x + 1 ...

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  9. Show that the relation R in the set {1, 2, 3} given by R= {(1, 2), (2,...

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  10. Give an example of a relation which is reflexive and transitive but no...

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  11. Show that the relation R in the set {1,2,3} defined as R={(1,3), (3, 2...

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  12. If R is the relation ‘less than' for: A= {2, 4, 6, 8, 10} to B= {8,...

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  13. If R is the relation '' greater than'' for : A = {1, 4, 5,} to B={1...

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  14. Show that the function f:N rarr N given by f(x) = 4x is one-one, but ...

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  15. Show that the function f:N rarr N given by f(x) = 5x is one-one but n...

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  16. Find fog and gof , if f(x) = x^2 , g (x) = x +1

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  17. If f :Rrarr R defined by f(x)= (5x+6)/7 is an invertible function, ...

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  18. Prove that the relation R in Z of integers given by: R = {(x, y): 2x -...

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  19. Prove that the relation R in Z of integers given by: R = {(x, y): 3x -...

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  20. Show that the relation R defined by R = {(a, b) (a - b), is divisible ...

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  21. Check the injectivity and surjectivity of the following function: f ...

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