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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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Any element of set `A`, say `x_i` can be connected with the element of set `B` in `p` ways. Hence, there are exactly `p^q` functions.
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RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. Write of the domain and range of f(x)=sqrt(x-[x])dot

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  2. Write the domain and range of function f(x) given by f(x)=sqrt([x]-x).

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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. Find the values of x for which the functions f(x)=3x^2-1 and g(x)=3+x ...

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  5. If f(x)="cos"((log)e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value ...

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  6. Let f(x)=|x-1|dot Then (a)f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c)f(...

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  7. If A={1,2,3},\ B={x , y} , then the number of functions that can be de...

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  8. If x!=1\ a n d\ f(x)=(x+1)/(x-1) is a real function, then f(f(f(2))) ...

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  9. If f: R->R : x!=0,\ -4lt=xlt=4 and f: A->A be defined by f(x)=(|x|)/x ...

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  10. If f: RrarrR and g: RrarrR are defined by f(x)=2x+3a n dg(x)=x^2+7, th...

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  11. If f: [-2, 2] -> R is defined by f(x)={-1,for -2<=x<=0 , then x...

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  12. If f(x)=64x^3+1/x^3 and alpha,beta are the roots of 4x+1/x=3. Then,f(a...

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  13. The domain of the function f(x)=sqrt(2-2x-x^2) is [-sqrt(3),\ sqrt(3)...

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  14. The domain of the function f(x)=sqrt[((x+1)(x-3))/(x-2)] is [-1,2)uu[3...

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  15. The domain of the function f(x)=sqrt(((x+1)(x-3))/(x-2)) is [-1,2)uu[3...

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  16. The domain of definition of the function f(x)=sqrt(x-1)+sqrt(3-x) is [...

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  17. The domain of definition of the function f(x)=sqrt((x-2)/(x+2))+sqrt((...

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  18. The domain of definition of the function f(x)="log"|x| is R b. (-oo...

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  19. The domain of definition of f(x)=sqrt[x-3-2sqrt(x-4)]-sqrt[x-3+2sqrt(x...

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  20. The domain of the function f(x)=sqrt(5|x|-x^2-6) is (a) (-3,\ -2)uu(...

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