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Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(...

Let `f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-(x))dot` Show that `g(x)ge0AAx in Rdot`

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ARIHANT MATHS-FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. If functions f:{1,2,…,n} rarr {1995,1996} satisfying f(1)+f(2)+…+f(199...

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  2. Find the range of y=sin^3x-6sin^2x+11sinx-6.

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  3. Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-(x))dot Show that g(...

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  4. If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

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  5. If f(x) is a real-valued function discontinuous at all integral points...

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  6. A function f from integers to integers is defined as f(x)={{:(n+3, n ...

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  7. If f:R->R and f(x)=sin(pi{x})/(x^4+3x^2+7), where {} is a fractional p...

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  8. Show that f: R→ R defined as f(a) = 3a – 4 is one to one function.

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  9. Find dy/dx if y= 3^x

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  10. Let y be element of the set A={1,2,3,,5,6,10,15,30} and x(1),x(2),x(3)...

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  11. If A gt 0, c,d,u.v are non-zero constants and the graph of f(x)=abs(Ax...

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  12. f(x)=x^(3)+3x^(2)+4x+bsinx+c cosx,forall x in R is a one-one function,...

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  13. If two roots of the equation (p-1)(x^2 +x +1)^2 -(p+1)(x^4+x^2+1)=0 ar...

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  14. If f(x)=x^11+x^9−x^7+x^3+1 and f(sin^(−1)(sin8))=α,α is constant, then...

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  15. Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...

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  16. The complete set of values of a for which the function f(x)=tan^(-1)(x...

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  17. The domain of the function f(x)=sin^(-1)""(1)/abs(x^(2)-1)+1/sqrt(si...

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  18. The domain of f(x)=(log(sin^(-1)sqrt(x^(2)+x+1)))/(log(x^(2)-x+1)) is ...

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  19. The domain of f(x)=sqrt(sin^(-1)(3x-4x^(3)))+sqrt(cos^(-1)x) is equal ...

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  20. The domain of the function f(x)=root(6)(4^(x)+8^(2//3(x-2))-52-2^(2(...

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