Let f^(prime)(x)>0 AA x in R and g(x...

Let `f^(prime)(x)>0 AA x in R and g(x)=f(2-x)+f(4+x).` Then g(x) is increasing in (i) `(-infty,-1)` (ii) `(-infty,0)` (iii) `(-1,infty)` (iv) none of these

A

`(-oo,1)`

B

`(-oo,0)`

C

`(-1,oo)`

D

None of these

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in

Let f'(x)>0AA x in R and g(x)=f(2-x)+f(4+x) Then g(x) is increasing in (i)(-oo,-1)( ii) (-oo,0)( iii) (-1,oo)( iv ) none of these

Let f''(x) gt 0 AA x in R and let g(x)=f(x)+f(2-x) then interval of x for which g(x) is increasing is

The exhaustive values of x for which f(x) = tan^-1 x - x is decreasing is (i) (1,infty) (ii) (-1,infty) (iii) (-infty,infty) (iv) (0,infty)

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

The domain of f(x)=log_x 12 is (i) (0,infty) (ii ) (0,1)cup (1,infty) (iii) (-infty,0) (iv) (2,12)

Let g'(x)>0 and f'(x)<0AA x in R, then

The solution set of the inequation ||x|-1| < | 1 – x|, x in RR, is (i)(-1,1) (ii)(0,infty) (iii)(-1,infty) (iv) none of these

f(x)=x^(2)-2x,x in R, and g(x)=f(f(x)-1)+f(5-f(x)) Show that g(x)>=0AA x in R