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Let f(x)=((2008)^x+(2008)^(-x))/2,g(x)=(...

Let `f(x)=((2008)^x+(2008)^(-x))/2,g(x)=((2008)^x-(2008)^(-x))/2` then prove that `f(x+y)=f(x)f(y)+g(x)g(y)`

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AAKASH INSTITUTE ENGLISH-RELATIONS AND FUNCTIONS -Assignment (Section - I) Subjective Type Questions
  1. Let f(x)=((2008)^x+(2008)^(-x))/2,g(x)=((2008)^x-(2008)^(-x))/2 then p...

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  2. Let g(x) be a function satisfying g(0) = 2, g(1) = 3, g(x+2) = 2g(x+1)...

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  3. Let g(x+(1)/(y)) + g(x-(1)/(y)) = 2g(x) g((1)/(y)) AA x, y in R, y !=0...

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  4. Let f : W-> W be a given function satisfying f(x) = f(x-1)+f(x-2) for...

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  5. Let f(x)=ln((1-x)/(1+x)) . Find x,y for which f(x)+f(y)=f((x+y)/(1+xy)...

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  6. The function f(x) satisfies the equation f(x + 1) + f(x-1) = sqrt3 f(x...

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  7. Let g : R rarr R be given g(x) = 3 + 4x. If g^(n)(x) = gogo.......ogo(...

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  8. Let f(x) = (e^(x) - e^(-x))/(2) and if g(f(x)) = x, then g((e^(1002) -...

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  9. Let f(x) be a function such that f(x + y) = f(x)+f(y) AA x, y in N and...

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  10. Let f(x) = (1)/(2) + sqrt((x-(3)/(4)) and phi(x) = f^(-1)(x) then phi(...

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  11. Let f : R rarr R and g : R rarr R be two given functions defined as f(...

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  12. about to only mathematics

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  14. Let f : R rarr R : f(x) = (2x-3)/(4) be an invertible function. Find f...

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  15. Prove that the relation R in set A = {1, 2, 3, 4, 5} given by R = {(a...

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  16. If functions f:A to B and g : B to A satisfy gof= I(A), then show that...

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  17. Find the domain and range of the real function f(x) = sqrt(4-x^(2))

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