Let `f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot` Show that `g(x)geq0AAx in Rdot`

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f: R->R be a twice differentiable function such that f(x+pi)=f(x) and f''(x)+f(x)geq0 for all x in Rdot Show that f(x)geq0 for all x in Rdot

f(x)=(1+x) g(x)=(2x-1) Show that fo(g(x))=go(f(x))

Let f(x) = 2x + 5. If x ne 0 then find (f (x +2) - f(2))/(x)

Let f:R→R:f(x)=x^2 and g: R→R: g(x)=(x+1) . Show that (gof)≠(fog) .

Let f(x)=2x+5 . If xne0 then find (f(x+2)-f(2))/(x)

If f(x)={1-|x|,|x|lt=1 0,|x|>1'a n dg(x)=f(x-1)+f(x+1), find the value of int_(-3)^3g(x)dxdot

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) be defined on [-2,2] and be given by f(x) = -1 , -2 <= x <= 0 1-x , 0 <= x <= 2 . and g(x)=f(|x|)+|f(x)|dot Then find g(x)dot

Consider f: R^(+)->R such that f(3)=1 for a in R^+ a n d """"f(x)dotf(y)+ f(3/x)f(3/y)=2f(x y)AAx ,y in R^+dot Then find f(x)dot