Q. 104.5( 2 Votes )

Mark the correct A. f(x) > 0 for all x ϵR

B. f(x) >f(x + 1) for all x ϵR

C. f(x) in invertible

D. f(x) < 0 for all x ϵ R

Answer :

Formula:- (i)The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f’(x)>0 for all x(a,b)


(ii)If f(x) is strictly increasing function on interval [a, b], then f-1 exist and it is also a strictly increasing function


Given:- f(x) = x3 – 6x2 + 15x + 3


=3x2-12x+15=f’(x)




Therefore f’(x) will increasing


Also f-1(x) is possible


Therefore f(x) is invertible function.

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