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

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.