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If f: R rightarrow R, f(x) is a differen...

If f: R rightarrow R, f(x) is a differentiable bijective function , then which of the following may be true?

A

`(f(x) -x)f'' ( x)lt 0, AA x in R `

B

`(f(x) -x)f''( x) gt 0, AA xx in R `

C

If `(f (x)-x)f'' (x) gt 0, ` then `f(x) =f^(-1) ` has no solution

D

If `(f (x) -x)f'' (x) gt 0," then " f(x) = f^(-1)(x) `

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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
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  3. The number of points in (-oo,oo) for which x^(2)-xsinx-cosx=0, is

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  14. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

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  16. If f(x)=e^(1-x) then f(x) is

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  17. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

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  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

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  19. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

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  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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