1.

Which of the following are True? (where [.] denotes greatest integer funstion)

Answer»

if `f(x)=[x],g(x)=|x-1|` then the VALUE of fog `(-7)/(4)+gof(-7)/(4)` is equal to 5
The number of solution of equation `|[x]-1|=x^(2)` is 2.
if `f^(2)(x)=x^(2)` then number of DIFFERENT POSSIBLE continuous FUNCTIONS `f(x)` is 4
if a polynomial function is invertible, then its inverse function is always differentiable.

Solution :
(A) fog `((-7)/(4))=f((11)/(4))=2`
`gof((-7)/(4))=g(-2)=|-2-1|=3`
(B) only ONE solution
(C). `|f(x)|=|x|`
`becausef(x)=x,|x|,-|x|`
(D). `f(x)=x^(3)`
`f^(-1)(x)=x^((1)/(3))` which is not differentiable at `x=0`


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