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If `f: AvecA ,g: Avec` are two bijections, then prove that `fog` is an injection (ii) `fog` is a surjection.

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If f: A->A ,g: A->A are two bijections, then prove that (i) fog is an injection (ii) fog is a surjection.

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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

Let f: R->R and g: R->R be two given functions such that f is injective and g is surjective. Then which of the following is injective? (a) gof (b) fog (c) gog (d) none of these

Let f : R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x)) then --(1) f is bijection (2) f is an injection only (3) f is a surjection (4) f is neither injection nor a surjection

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If A={1,\ 2,\ 3,\ 4} and B={a ,\ b ,\ c ,\ d} . Define any four bij...

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  2. Let A and B be two sets each with a finite number of elements. Assume ...

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  3. If f: AvecA ,g: Avec are two bijections, then prove that fog is an inj...

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  4. If f: A->A ,\ \ g: A->A are two bijections, then prove that fog is an ...

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  5. Which one of the following graphs represent a function? (FIGURE)

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  6. Which one of the following graphs represent a one-one function? (FI...

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  7. Let A={1,\ 2} and B={a ,\ b} be two sets. Write total number of one-...

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  8. Write total number of one-one functions from set A={1,\ 2,\ 3,\ 4} ...

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  9. If f: R->R is defined by f(x)=x^2 , write f^(-1)(25) .

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  10. If f: C->C is defined by f(x)=x^2 , write f^(-1)(-4) . Here, C denotes...

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  11. If f: R->R is given by f(x)=x^3 , write f^(-1)(1) .

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  12. Let C denote the set of all complex numbers. A function f: C->C is def...

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  13. Let f be a function from C (set of all complex numbers) to itself g...

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  14. Let f: R->R be defined by f(x)=x^4 , write f^(-1)(1) .

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  15. Find the derivative of f(x)=x^4

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  16. If f: R->R is defined by f(x)=x^2 , write f^(-1)(25) .

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  17. If f: C->C is defined by f(x)=(x-2)^3 , write f^(-1)(-1) .

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  18. If f: R->R is defined by f(x)=10 x-7 , then write f^(-1)(x) .

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  19. Let f:{-pi/2,\ pi/2}->R be a function defined by f(x)=cos[x]dot Write ...

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  20. If f: R->R defined by f(x)=3x-4 is invertible then write f^(-1)(x) .

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