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Let f : R to R be the signum function d...

Let `f : R to R` be the signum function defined as `f(x) = {{:(1, x gt 0),(0, x =0),(-1, x lt 0):}` and `g: R to R` be the greatest integer function given by `g(x) = [x]` where [x] is greatest integer less than or equal to x. Then, does fog and gof coincide in (0,1] ?

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
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  2. Consider f : R+ rarr (-9, infty) given by f(x) = 5x^2 + 6x - 9. Prove ...

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  3. Let f : R to R be the signum function defined as f(x) = {{:(1, x gt 0...

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  6. If f : R rarr R is defined by f(x) = x^2 – 3x + 2, find f (f (x)).

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  7. If f : R rarr R is defined by f(x) = x^2 – 3x + 2, find f (f (x)).

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  8. If f : R rarr R is defined by f(x) = x^2 – 3x + 2, find f (f (x)).

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  9. Show that *:RxxRrarrR, given by (a,b)rarra+4b^2 is a binary operation...

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  10. Let a mapping '*' from R xx R to R be defined by a * b = 2 a + 2 b for...

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  12. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  13. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  14. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  15. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  16. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  17. Consider the operations '*' and o+ on the set R of all real numbers de...

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  18. Consider the operations '*' and o+ on the set R of all real numbers de...

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  19. Consider the operations '*' and o+ on the set R of all real numbers de...

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