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If a , b are two fixed positive integers...

If `a , b` are two fixed positive integers such that `f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3)` for all real `x ,` then prove that `f(x)` is periodic and find its period.

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A DAS GUPTA-Function-Exercise
  1. If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^...

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  2. Let f(x)=(ax+b)/(cx+d) , x!=-d/c. If d=-a, show that f{(x)}=x is an ...

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  3. If f(x)=loge(x+sqrt(1+x^2) , g(x)=loge(1+sqrt(1+x^2)and h(x)=f(x)-g(x...

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  4. Find the natural number a for which sum(k=1)^n f(a+k)=16(2^n-1) wher...

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  5. Find the domain of f(x)=sqrt(x^2-4x+3)

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  6. Find the domain off(x)=1/sqrt(x^2-x-2)

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  7. Find the domain of f(x)=1/(sqrt(x-|x|))

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  8. Find the domain off(x)=sqrt(((x+1)(x-3))/(x-2)

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  9. Find the domain of f(x) = sqrt(log(10)((3-x)/x))

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  10. Find the domain off(x)=sin^-1{log2(1/2x^2)}

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  11. Find the domain ofy=cos^-1((3+sinx)/4)

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  12. Find the domain off(x)=sqrt(5(|x|-x^2-6)

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  13. Find the domain ofy=cos^-1{x[x[}

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  14. Find the domain off(x)=log2x-5(x-3x-10)

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  15. Find the domain of the real-valued functions: f(x)=sqrt(4-x)+sqrt(x-5)

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  16. Find the domain of the real-valued functions: f(x)=sqrt(3-x)+cos^-(1)(...

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  17. Find the domain of the real-valued functions: y=sin^-1x+sqrt(2x-x^2)-1...

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  18. If log(x)y.log(xy)y.log(x^2y)y=1/6 then express y as the real function...

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  19. f(x) is defined over [0,1]. Find the domain of the function f(2x+3)

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  20. The function f(x) is defined on the interval [0, 1]. Find the domain ...

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  21. f(x) is defined over [0,1]. Find the domain of the function f(cosx)

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