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If 2f(x) - 3f(1/x) =x^2 (x ne 0), then f...

If 2f(x) - 3f(1/x) =`x^2 (x ne 0)`, then find f(2).

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PATHFINDER-FUNCTIONS-QUESTION BANK
  1. If f(x) = sin x + cos x , g(x) =x^2 - 1 then show that g(f(x)) is inve...

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

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  3. If 2f(x) - 3f(1/x) =x^2 (x ne 0), then find f(2).

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  4. If f(x) =cos[pi^2]x + cos[-pi^2]x, where [x] stands for the greatest i...

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  5. Find the range of f(x)=(x^2 + x +2)/(x^2 + x +1) (-infty lt x lt infty...

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  6. Find the domain of definition of the function f(x) = 1/sqrt(absx + x).

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  7. If f : RrarrR such that f(x) = x - [x], where [p] denotes the greatest...

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  8. Find the range of the function f(x) = x^2 + 1/(x^2 + 1).

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  9. Find the range of the function phi where phi(x) = cos^-1 (x^2/(1 + x^2...

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  10. Find the range of the function f(x) =abs(x - 1) + abs(x - 2) , -1 le x...

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  11. Find the range of the function y = log3 (5 + 4x - x^2).

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  12. If f(x + y) = f(x) - f(y),forall x, y in R, then show that f(3) = f(1)

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  13. Find the range of the function f(x) = (e^x - e^-x).

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  14. Find the inverse function of the function f(x) = [4 - (x - 7)^3]^(1/5)...

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  15. If f(x) =e^(x + a) , g(x) = x^(b^2) and h(x) = e^(b^2 x), then find th...

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  16. Find domain of the function f(x) = 2^sin^(-1)x + 1/sqrt(x - 2).

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  17. Prove that the domain of g(x) =cot^-1 x/sqrt(x^2 - [x]) , x in R is R ...

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  18. Find the range of the function y =1/(2 - cos 2x).

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  19. Find the range of the function y = log2 (sin x + cos x + 3sqrt2)/sqrt2

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  20. Find the value of x which f(x) = 1/sqrt(absx - x) is not defined.

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