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If f: A->B and g: B->C are one-one fun...

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

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If f: AvecBa n dg: BvecC are one-one functions, show that gof is one-one function.

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

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

What is meant by one-one function?

Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

If f and g are one-one functions, then a. f+g is one one b. fg is one one c. fog is one one d. none of these

Show that if f : A ->B and g : B ->C are one-one, then gof : A ->C is also one-one.

If fa n dg are one-one functions, then (a) f+g is one one (b) fg is one one (c) fog is one one (d) non e of t h e s e

Let A be a finite set. If f: A->A is a one-one function, show that f is onto also.

Let A be a finite set. If f: A->A is an onto function, show that f is one-one also.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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

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

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

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  5. 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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  6. 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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  7. If f(x)=e^x and g(x)=(log)e x(x >0), find fog and gof. Is fog=gof?

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

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

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

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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 (f+2g)(-1)

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

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

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

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

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

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

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  20. Find fog and gof , if f(x)=x^2 , g(x)=cosx

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