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If `f(x)=(a^x+a^(-x))/2` and `f(x+y)+f(x-y)=kf(x)f(y)` then `k=`

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MCGROW HILL PUBLICATION-SETS, RELATIONS AND FUNCTIONS-SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS )
  1. Let A and B be two finite sets and let P(A) and P(B) respectively deno...

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  2. Suppose f: R -{5//3} to R - {5//3} is given by f(x) = (5x+a)/(3x-5). I...

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  3. Suppose f:[1,infty) to [1, infty) is defined by f(x) = 1/2(1+ sqrt(1+4...

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  4. Let f: R - {0} to R be defined by f(x) = x+ 1/x, then 7 + f((x))^(4...

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  5. If A = {a, b, c, d}, then the number of functions on the set A which a...

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  6. Suppose A and B are two sets such that A contains 5 elements and B - A...

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  7. Suppose P{S) denote the power set of the set S. Let A = {1}. If the nu...

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  8. Let g(x) = x^(2) + x -1 AA x in R and (gof)(x) = 4x^(2) + 10 x + 5 AA ...

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  9. Let X = {n in N :1 le n le 50}. If A = {n in X: " n is a multiple of 2...

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  10. Let S be the set of all real roots of the equation,3^(x)(3^(x)-1)+2=|3...

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  11. Let W = N cup {0}. Suppose f : W to W is a function such that f(0)=0, ...

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  12. Let S = {1, 2, 3, 4, 5}. The number of ordered pairs of subsets (A, B)...

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  13. The number of equivalence relations that can be defined on set {a, b, ...

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  14. Let A = {a, b, c, d}. The number of invertible functions f: A to A sat...

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  15. Define f: R to R by f(x) = (sin^(2)x + cos^(4)x)/(cos^(2)x + sin^(4)...

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  16. For x in R -{-1/n, n in N}, define f(x) = lim(n to infty)(x/(x+1) + x/...

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  17. If f(x)=(a^x+a^(-x))/2 and f(x+y)+f(x-y)=kf(x)f(y) then k=

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  18. Let f,g : R to R be defined by f(x) = (x-2)|x-2| AA x in R g(x) = s...

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  19. Define f : R to R by f(x) = 4 cos^(4)((x-pi)/(4pi^(2))) - 2 cos((x-p...

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  20. Let f(x) =1/x, g(x) = 1/(9x^(2)-1) and h(x) = (11x)/(x+3) be three fun...

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