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Let A and B be any two sets such that n(...

Let A and B be any two sets such that n(B)=P, n(A)=q then the total number of functions f:` A -> B` is equal to

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To find the total number of functions \( f: A \to B \) where \( n(A) = q \) and \( n(B) = p \), we can follow these steps: ### Step-by-Step Solution 1. **Understanding the Sets**: - Let \( A \) be a set with \( q \) elements. - Let \( B \) be a set with \( p \) elements. ...
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RD SHARMA ENGLISH-FUNCTION-All Questions
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  2. 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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  3. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

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

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  6. Which one the following relations on A={1,2,3} is function? f={(1,3),(...

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  7. Write the domain of the real function f defined by f(x)=sqrt(25-x^2) .

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  8. Let A}x :-1lt=xlt=1}a n df: Avec A such that f(x)=x|x|, then f is (a) ...

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  9. If the function f:[1,oo)rarr[1,oo) is defined by f(x)=2^(x(x-1)),t h e...

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

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

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  12. Let f: R-> R be the function defined by f(x)=4x−3 for all x in R. Then...

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  13. Find whether f: R->R given by f(x)=x^3+2 for all x in R .

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  14. Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

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  15. Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , i...

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  16. Discuss the surjectivity of f: R->R given by f(x)=x^3+2 for all x i...

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  17. Discuss the surjectivity of f: R->R given by f(x)=x^2+2 for all x i...

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  18. Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in...

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  19. Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for e...

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  20. Show that the Signum function f:R->R, given by f(x)={(1,xgt0),(0,x=0),...

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