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Let f(x)=(2cosx-1)(2cos2x-1)(2cos2^2x-1)...

Let `f(x)=(2cosx-1)(2cos2x-1)(2cos2^2x-1)(2cos2^n x-1),` (where `ngeq1)dot` Then prove that `f((2pik)/(2^n+-1))=1AAk in Idot`

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FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-I
  1. Find the range of the following functions: y = 2 + sinx

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  2. Find the range of the following functions: y=1/(2-cos3x)

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  3. Find the range of log3{log(1/2)(x^2+4x+4)}

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  4. Find the range of the following functions: y=sqrt(6-x)+2sqrt(x-4)

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  5. Find the range of the following functions: f(x)=(e^(x))/(1+absx),xg...

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  6. Find the range of the following functions: f(x)=[ln(sin^(-1)sqrt(x^...

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  7. Find the period f(x)=sinx+{x}, where {x} is the fractional part of xdo...

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  8. Find the period of the following, if exists: f(x) = tan3x + sin(x/3)

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  9. Find the period of the following, if exists: f(x)=e^(3"in"e^(x)-[3x]...

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  10. Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):}and g(x)={(x-3","...

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  11. A function defined for all real numbers is defined for x>-0 as follows...

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  12. Let f(x)={{:(1+x,0lexle1).(3-x,1ltxltoo):} Define f(f(x)). AIso obta...

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  13. Find the domain of the function, f(x)=log{log(abs(sinx)){x^(2)-8x+23...

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  14. Prove that function f(x)=cos sqrt(x) is non-periodic.

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  15. If f is symmetrical about x = 1, find the real values of x satisfying ...

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  16. If f(x) is an even function and satisfies the relation x^(2)f(x)-2f(1/...

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  17. let f(x) be a polynomial satisfying f(x) : f(1/x) = f(x) + f(1/x) for ...

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  18. Let n be a positive integer with f(n) = 1! + 2! + 3!+.........+n! and ...

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  19. Let f(x)=(x(sinx+tanx))/([(x+pi)/(pi)]-1//2) (where (.] denotes the gr...

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  20. Let f(x)=(2cosx-1)(2cos2x-1)(2cos2^2x-1)(2cos2^n x-1), (where ngeq1)do...

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