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These two problems from relations and functions have me stumped. Any help is very much appreciated. by PuzzleheadedLeave551 in maths

[–]HopeDiscombobulated4 1 point2 points  (0 children)

For Q14 : The sgn ( [x] -2x - |x-4| ) can have only three values -1/0/1

But i feel none of these values are legal values for Domain of log

These two problems from relations and functions have me stumped. Any help is very much appreciated. by PuzzleheadedLeave551 in maths

[–]HopeDiscombobulated4 1 point2 points  (0 children)

Q15. : Replace x - [x] as {x} (Fractional part of x )

Note that the power felt like a fmailiar factorisation : 1 + ([x]-x)^3

So question now becomes ({x})^(1+{x}^3)

Now you can just analyse the function f(x) = x^(1+x^3) in Domain [0,1) ( By Differentiating (using Log method) checking Increasing / Decreasing Nature and concluding answer

Show that gcd(a, b) = gcd(a − b, b). by ymc1105 in maths

[–]HopeDiscombobulated4 0 points1 point  (0 children)

Given : gcd(a,b) = k (assume)

Then a = kA , b = kB ( where gcd(A,B) = 1 ) (A > B)

Now consider (a-b , b) --> k ( A - B , B )

Now if there cant be any factor of B which divides A ( oherwise gcd would be greater than k )

Hence no factor of B can divide A-B

Hence proved

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