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Give examples of two functions `f:" "N->Z" "a n dg:" "Z->Z` such that o f is injective but is not injective. (Hint: Consider `f(x)" "=" "x" "a n d""""""""g(x)" "=" "|x|` )

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

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  2. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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  3. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  4. If f: A->B and g: B->C are one-one functions, show that gof is one-o...

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  5. If f: A->B and g: B->C are onto functions, show that gof is an onto fu...

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  6. If f: R->R and g: R->R be functions defined by f(x)=x^2+1 and g(x)=sin...

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  7. If f:[0,oo)->R and g: R->R be defined as f(x)=sqrt(x) and g(x)=-x^2-1,...

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  8. If f(x)=e^x and g(x)=(log)e x(x >0), find fog and gof. Is fog=gof?

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  9. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

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  10. If f(x)=1/x and g(x)=0 are two real functions, show that fog is not...

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  11. Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

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  12. Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

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  13. Let f(x)=[x] and g(x)=|x| . Find (f+2g)(-1)

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  14. Let fa n dg be real functions defined by f(x)=x/(x+1)a n dg(x)=1/(x+3)...

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  15. If f(x)=(3x-2)/(2x-3), prove that f(f(x)))=x for all x in R-{3/2} .

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  16. If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , p...

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  17. If f(x) = x/(sqrt(1+x^2) then fofof(x)

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  18. Let f be a real function defined by f(x)=sqrt(x-1) . Find (fofof)(x...

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  19. If f(x)=(x-1)/(x+1),x!=-1, then show that f(f(x))=-1/x provided that x...

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  20. Find fog and gof , if f(x)=e^x , g(x)=(log)e x

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