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Find the integral solutions to the equat...

Find the integral solutions to the equation `[x][y]=x+y` . Show that all the non-integral solutions lie on exactly two lines. Determine these lines. Here [.] denotes greatest integer function.

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Integral solutions are (2,2) and (0,0) , all non-integral solutions lie on exactly two lines x+y=0 and x+y=6.
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ARIHANT MATHS-FUNCTIONS-Exercise For Session 4
  1. f(x)=sqrt(x^(2)-abs(x)-2) . Find the domain of f(x).

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  2. f(x)=sqrt(2-abs(x))+sqrt(1+abs(x)). Find the domain of f(x).

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  3. f(x)=log(e)abs(log(e)x). Find the domain of f(x).

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  4. f(x)=sin^(-1)((2-3[x])/4), which [*] denotes the greatest integer func...

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  5. f(x)=log(x-[x]), where [*] denotes the greatest integer function. find...

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  6. f(x)=1/sqrt([x]^(2)-[x]-6), where [*] denotes the greatest integer fun...

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  7. f(x)= cosec^(-1)[1+sin^(2)x], where [*] denotes the greatest integer f...

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  8. f(x)=cos^-1sqrt(log([x]) ((|x|)/x)) where [.] denotes the greatest int...

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  9. f(x)=sqrt((x-1)/(x-2{x})), where {*} denotes the fractional part.

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  10. Domain of f(x)=sin^(-1)(([x])/({x})), where [*] and {*} denote greates...

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  11. f(x)=sin^(-1)[2x^(2)-3], where [*] denotes the greatest integer funct...

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  12. f(x)=sin^-1[log2(x^2/2)] where [ . ] denotes the greatest integer func...

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  13. The domain of f(x) = sqrt( 2 {x}^2 - 3 {x} + 1) where {.} denotes the...

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  14. f(x)=1/([abs(x-2}]+[abs(x-10)]-8) where [*] denotes the greatest integ...

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  15. If a function is defined as f(x)=sqrt(log(h(x))g(x)), where g(x)=|sinx...

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  16. The number of solutions of the equation [y+[y]]=2 cosx, where y=(1)...

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  17. Prove that for n=1, 2, 3... [(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+...

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  18. Find the integral solutions to the equation [x][y]=x+y . Show that all...

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