Let `g(x)=f(x)+f(1-x)` and `f "(x)>0AAx in (0,1)dot` Find the intervals of increase and decrease of `g(x)dot`

Let g(x)=f(logx)+f(2-logx)a n df^(x)<0AAx in (0,3)dot Then find the interval in which g(x) increases.

Let g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot Then g(x) increases in (a) (1/2,2) (b) (4/3,2) (c) (0,2) (d) (0,4/3)

Discuss the monotonocity of Q(x), where Q(x)=2f((x^2)/2)+f(6-x^2)AAx in R It is given that f'(x)>0AAx in Rdot Find also the point of maxima and minima of Q(x)dot

Let f(x)=x+f(x-1)forAAx in RdotIff(0)=1,fin df(100)dot

Find the interval of monotonocity of the function f(x)=|x-1|/x^2dot

If f(x) and g(x)=f(x)sqrt(1-2(f(x))^2) are strictly increasing AAx in R , then find the values of f(x)dot

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then find the value of f(7)dot

Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical about. (a)The origin (b) the line x=1/2 the point (1,0) (d) the point (1/2,0)

f( x )={ x+1,x 0 and g(x)={ x 3 x 1 find f(g(x)) and its domain and range

Let f(x)=sqrtx and g(x)=x be two functions defined over the set of non-negative real numbers. Find (f+g) (x), (f-g), (fg) (x) and (f/g) (x) .