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If f(x)=cos(logx), then show that f((1)/...

If `f(x)=cos(logx)`, then show that `f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/(y))+f(xy)]=0`

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AAKASH SERIES-FUNCTIONS -EXERCISE -1.1 (VERY SHORT ANSWER QUESTIONS)
  1. Is g={(1,1),(2,3),(3,5),(4,7)} is a function from A={1,2,3,4}. to B={1...

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  2. If f= {(1, 2), (2, -3), (3, -1)} then find: (i) 2f, (ii) 2+f, (iii) ...

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  3. If f={(4,5),(5,6), (6,-4)} and g={(4,-4),(6,5),(8,5)} then find: (i)...

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  4. If f(x) = x^(2) and g(x) = Ixl then find the values of: (i) f+g, (i...

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  5. If f: R - {0} to R is defined by f(x) = x^(3)-1/(x^3), then S.T f(x) +...

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  6. f:R-{0} to R is defined as f(x)=x+1/x then show that (f(x))^(2)=f(x^(2...

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  7. If f:R-(pm1)toR is defined by f(x)=log|(1+x)/(1-x)|, then show that f(...

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  8. If f(x)=cos(logx), then show that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/...

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  9. If the function f: R to R defined by f(x)=(4^(x))/(4^(x)+2), then show...

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  10. If the function f: R to R defined by f(x)=(3^(x)+3^(-x))/(2), then S....

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  11. If f: R to R, g : R to R are defined by f(x) = 4x-1 and g(x) = x^(2)+2...

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  12. If f: R to R, g : R to R are defined by f(x) =3x-1, g(x) =x^(2)+1, the...

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  13. If f(x)=(x)/(sqrt(1-x^(2))), g(x)=(x)/(sqrt(1+x^(2))) then (fog)(x)=

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  14. If f(x) = 1//x, g(x) = sqrt(x) for all x in (0,oo), then find (gof)(x)...

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  15. If f(x) = 2, g(x) = x^(2), h(x) = 2x then find (fogoh)(x)

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  16. If f(x) = (x+1)/(x-1) (x ne -1) then find (fofof)(x) and (fofofof)(x).

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  17. Let f(x) = x^(2), g(x) = 2^(x). Then solve the equation (fog)(x)=(gof)...

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  18. Determine whether the following functions are even or (odd). (i) f(x...

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  19. P.T the real valued function f(x)= (x)/(e^(x)-1) + x/2 + 1 is an even ...

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  20. If f:R to R is defined as f(x+y)=f(x)+f(y) AA x,y in R and f(1) = 7, f...

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