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A function `f (x)` is defined for all `x in R` and satisfies, `f(x + y) = f (x) + 2y^2 + kxy AA x, y in R`, where `k` is a given constant. If `f(1) = 2 and f(2) = 8`, find `f(x)` and show that `f (x+y).f(1/(x+y))=k,x+y != 0`.

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ARIHANT MATHS-FUNCTIONS-Exercise (Single Integer Answer Type Questions)
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  2. If f:R rarr R satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all x,y i...

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  3. Let f:N rarr R be such that f(1)=1 and f(1)+2f(2)+3f(3)+…+nf(n)=n(n+1)...

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  4. If f(x)=(2010x+165)/(165x-2010), x gt 0 " and " x ne (2010)/(165), the...

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  5. If alpha,beta,gamma in R, alpha+beta+gamma=4 " and " alpha^(2)+beta^(2...

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  6. The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in R...

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  7. If A={1,2,3}, B={1,3,5,7,9}, the ratio of number of one-one functions ...

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  8. If n(A)=4, n(B)=5 and number of functions from A to B such that range ...

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  9. If a and b are constants, such that f(x)=asinx+bxcosx+2x^(2) and f(2...

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  10. If the functions f(x)=x^(5)+e^(x//3) " and " g(x)=f^(-1)(x), the value...

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  11. If f(x)=x^(3)-12x+p,p in {1,2,3,…,15} and for each 'p', the number of ...

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  12. Let f(x) denotes the number of zeroes in f'(x). If f(m)-f(n)=3, the va...

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  13. If x^2+y x^2=4 then find the xamimum value of (x^3+y^3)/(x+y)

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  14. Let f(n) denotes the square of the sum of the digits of natural numbe...

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  15. If [sinx]+[x/(2pi)]+[(2x)/(5pi)]=(9x)/(10pi), where [*] denotes the gr...

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  16. The number of integral solutions of 1/x+1/y=1/6 " with " x le y " is "...

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  17. If f(x) is a polynominal of degree 4 with leading coefficient '1' sati...

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  18. If a+b = 3- cos 4 theta and a-b =4 sin 2theta, then ab is always less ...

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  19. Let 'n' be the number of elements in the domain set of the function f(...

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  20. If f(x) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x) and f(5)=10,...

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