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If R is the set of real numbers prove th...

If R is the set of real numbers prove that a function `f: R -> R,f(x)=e^x , x in R` is one to one mapping.

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NAGEEN PRAKASHAN ENGLISH-RELATIONS AND FUNCTIONS -Exercies 1b
  1. f: R to R is a function where f(x)= 2x-3 . Check whether f is noe -on...

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  2. The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)} on set A={1,2,3} ...

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  3. Show that the function f: N->N , given by f(x)=2x , is one-one but not...

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  4. The function f:R to R defined as f(x)=x^(2). The function f is

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  5. If Q is the set of rational numbers, then prove that a function f: Q t...

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  6. If R is the set of real numbers then prove that a function f: R to R ...

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  7. Prove that the function f: R^(+) to R which is defined as f(x)=log(e)...

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  8. If R is the set of real numbers prove that a function f: R -> R,f(x)=...

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  9. A function f: R to R is defined as f(x)=4x-1, x in R, then prove that...

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  10. Let A=R-{3}a n dB=R-{1}dot Consider the function f: Avec defined by f(...

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  11. Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show th...

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  12. If a function f: R to R is defined as f(x)=x^(3)+1, then prove that f...

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  13. If A={x : x in R, (-pi)/(2) le x le (pi)/(2)}, B={y : y in R, -1 le y ...

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  14. If f: R to R and g : R to R be two functions defined as respectivel...

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  15. Function f: R to R and g : R to R are defined as f(x)=sin x and g(x) ...

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  16. If f: R to R and g: R to R be two functions defined as f(x)=2x+1 an...

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  17. If f and g are two functions from R to R which are defined as f(x)=x^(...

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  18. If f: R to R and g: R to R be two functions defined as f(x)=x^(2) an...

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  19. If f: R to R defined as f(x)=3x+7, then find f^(-1)(-2)

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  20. If Q is the set of rational numbers and a function f:Q to Q is define...

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