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Let f: Rvec and g: RvecR be defined +1a ...

Let `f: Rvec` and `g`: RvecR` be defined +1a n dg(x)=x-1.` Show that `fog=gof=I_Rdot`

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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

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  2. Let A={1,2} . Find all one-to-one function from A to A.

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  3. Let f: Rvec and g: RvecR be defined +1a n dg(x)=x-1. Show that fog=gof...

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  4. Verify assoiativity for the following three mappings : f: NvecZ0...

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  5. If the set A contains 5 elements and the set B contains 6 elements, t...

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  6. If the set A contains 7 elements and the set B contains 10 elements, ...

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  7. f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-on...

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  8. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

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  9. Let A={1,2,3}dot Write all one-one from A to itself.

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  10. If f: RvecR be the function defined by f(x)=4x^3+7, show that f is a b...

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  11. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

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  12. The value of parameter alpha, for which the function f(x) = 1+alpha x,...

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  13. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

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  14. Show that the function f: R ->R is given by f(x)=1+x^2 is not invertib...

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

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  16. 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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  17. Let f: NvecS be a function defined as f(x)=4x^2+12 x+15. Show that f: ...

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  18. Let A=R-{3} and B=R-[1]dot Consider the function f: AvecB defined by f...

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  19. Let f,g:vec R be defined by f(x)=2x+1 and g(x)=x^2-2 for all x in R, r...

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  20. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

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