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Let `f: Nvec` be a function defined as `f(x)=9x^2+6x-5.` Show that `f: NvecS ,` where `S` is the range of `f,` is invertible. Find the inverse of `f` and hence `f^(-1)(43)` and `f^(-1)(163)dot`

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A=R-{3}a n dB=R-{1}dot Consider the function f: Avec defined by f(...

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  2. Consider f:R+->[-9,oo[ given by f(x)=5x^2+6x-9. Prove that f is invert...

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  3. Let f: Nvec be a function defined as f(x)=9x^2+6x-5. Show that f: Nvec...

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  4. If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is inve...

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  5. If f: R->(0,\ 2) defined by f(x)=(e^x-e^(-x))/(e^x+e^(-x))+1 is invert...

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  6. Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f i...

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  7. Let A={x in R|-1lt=xlt=1} and let f: A->A ,\ g: A->A be two functions...

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  8. Let f be a function from R to R such that f(x)=cos(x+2) . Is f inverti...

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  9. If A={1,\ 2,\ 3,\ 4} and B={a ,\ b ,\ c ,\ d} . Define any four bij...

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

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

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

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

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

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

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

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

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

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

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

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