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The polynomial f(x) is defined by f(x)...

The polynomial f(x) is defined by
`f(x)={{:("0 when x is an integer ,"),("1 when x is not an integer ,"):}`
Then compute : `(a)f(-2),(b)f(sqrt3)`.

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CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.2
  1. If f(x)=(1-x)/(1+x), then prove that f(x)+f(1/x)=0.

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  2. Find the zeroes of the polynomial p(x)=x^(2)-(a+1/a)x+1.

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  3. If f(x)=log(2)xandg(x)=x^(2) then find f(g(2)).

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  4. If f(x)=x^(2)andg(x)=sqrtx, then prove that g(f(4)) = 4.

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  5. If f(x)=4^(x), then prove that (f(x+1))/(f(x-1))=16.

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  6. The polynomial f(x) is defined by f(x)={{:("0 when x is an integer ,...

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  7. If the polynomial f(x) be defined by f(x) = {{:(2x^(2)-3 " when " xl...

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  8. If f(x) = ax + b, f(0) = 2 and f(4) = 10, then find the values of a an...

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  9. If 2f(x) + 3f(-x) = 15 - 4x, then prove that f(x) = 3 + 4x.

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  10. If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the va...

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  11. If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values...

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  12. If f(x)=1/(4x^(2)), then proved that (f(x-h)-f(x+h))/h=x/((x^(2)-h^(2)...

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  13. If y=f(x)=(2x+3)/(5x-a), then determine the value of a so that x = f(y...

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  14. If f(x) = (x-1)/(x+1), then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/...

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  15. If 2f(x-1)-f((1-x)/x)=x, then prove that 3f(x)=2(x+1)+1/(x+1).

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  16. If xgt0, then prove that the value of the polynomial (2x+2^(-x)-2) is ...

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  17. If f(x)=(x-a)/x+x/(x-b), then find f((a+b)/2).

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  18. If 3f(x)-f(1/x)=log(e)x^(4)(xgt0), then prove that f(e^(x))=x.

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  19. If f(x)=x^(9)-2x^(8)-2x^(6)+4x^(5)+x^(4)-2x^(3)+x-1, then find the val...

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  20. If f(x)=(a-x^(n))^(1/n),agt0 and n is a positive integer, then prove t...

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