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If f(x)={{:(2x^(2)+3" when " x le 2,),(2...

If `f(x)={{:(2x^(2)+3" when " x le 2,),(2x+1 " when "2 lt x le 3,),((1)/(2x-1) " when "x gt 3,):}` then f( e) =

A

`2e^(2) - 3`

B

2e + 1

C

`1/(2e-1)`

D

None of these

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CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.2
  1. If f(x)={{:("0, when x is an integer ,"),("2, when x is not an integer...

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  2. If f(x)={{:("2x+3, when x is an rational ,"),(x^(2)+1", when x is irra...

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  3. If f(x)={{:(2x^(2)+3" when " x le 2,),(2x+1 " when "2 lt x le 3,),((1)...

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  4. If p(x + 1) = x + 4, then find the value of [p(1) + p(-1)] is

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  5. The zeros of the polynomial p(x)=x^(2)-9 are

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  6. If (2x-1)^(8)=a(8)x^(8)+a(7)x^(7)+a(6)x^(6)+..........+a(1)x+a(0), the...

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  7. If g(x-2)=x^(2)-4x+5, the determine - (a) g (x) and (b) g(x + 1).

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  8. If h(x)=(x^(3)-a^(3))/(x-a), then find h(a).

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  9. If f(x)=(4+x)/(4-x), then find f(2^(-1)).

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  10. If f(x)=4^(x)/(4^(x)+2) then find f(x) + f(1 - x).

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  11. If f(x)=x/(2^(x)-1), then show that f(-1) = 2.

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  12. What is the zero of the polynomial p(x)=(x^(n)-1)/(2^(x)-1), where n i...

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  13. Determine the zeroes of the polynomial p(x)=x^(2)-5x.

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  14. Find the zeroes of the polynomial p(x)=x^(2)-5x+4.

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  15. Determine f(x), when f(x+3)=2x^(2)-3x-1.

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  16. If y=f(x)=(ax+b)/(cx-a), then find f(y).

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  17. If f(x)=2^(ax+1), the determine f(a)*f(b)*f(c).

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  18. If f(x)=x^(2)-5x+6, then determine f(x^(2)+1).

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  19. If f(x)=2^(x), then prove that f(x +1) = 4f( x - 1).

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  20. If f(x)=(1-x)/(1+x), then prove that f(x)+f(1/x)=0.

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