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If f(x) = cos(loge x), then find the val...

If f(x) = `cos(log_e x)`, then find the value of f(x)`cdot f(y) - 1/2[f(x/y) + f(xy)]`

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PATHFINDER-FUNCTIONS-QUESTION BANK
  1. Find the value of x which f(x) = 1/sqrt(absx - x) is not defined.

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  2. Find the range of y=x/(1 + x^2)

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  3. If f(x) = cos(loge x), then find the value of f(x)cdot f(y) - 1/2[f(x/...

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  4. Find the domain of f(x) = sin^-1 [ log9(x^2/4)]

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  5. Without using graph paper the graph of the function y = f(x) = abs(x -...

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  6. Without using graph paper draw a sketch graph of the function f(x) = 2...

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  7. Find the domain of the function F(x) = tan^-1 sqrt(x(x + 1)) + sin^-1 ...

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

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  9. Find the domain of function f(x) = cos^-1 ((2 - absx)/4) + 1/log(3 - x...

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  10. If 2f(x) + 3f(-x) = 15 - 4x for all real values of x , then show that ...

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  11. If 2f(x - 1) - f((1-x)/x) = x find f(x).

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

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  13. If f(n + 1) = (2f(n) + 1)/2 , n = 1,2,3,....... and f(1) = 2, then fin...

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  14. f(x) = (alpha x)/(x + 1) (x ne -1), then for what value of alpha , f{f...

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  15. Find the range of f(x) = ^(7 - x) P(x - 3).

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  16. Find the inverse function of the function f(x) = 2^(x(x - 1)) (x gt 0)...

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  17. If f(x) =log e (1 + x)/(1 - x) and g(x) = (3x + x^3)/(1 + 3x^2), then ...

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  18. If f(x) = ax^2 + bx + c find a, b so that f(x + 1) = f(x) + x + 1 may ...

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  19. c is any real number and c ne 0. Prove that abs(f(c) - f(-c)) = 2, whe...

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  20. Find the range of f(x) =3 sin sqrt(pi^2/16 - x^2).

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