Consider `f(x) = |x||x -1 | x - 2| x - 3| AA x in [1, 2]` and `g(x) = | x |+ |x – 1|+ |x - 2| + |x - 3| AA x ein (- oo, oo)`.If max. `f(x) = lambda min g(x)` at `x = x_a` then `(lambda + x_a)` is equal to

If f(x) = [x - 8] " & " g(x) = f(f(x)) AA x > 16 then g^1(x) equals

If f (x) =|x-5| and g (x) =f (f (x)) AA x gt 10, then g' (x) equals

If f (x) =sin x+cos x, x in (-oo, oo) and g (x) = x^(2), x in (-oo,oo) then (fog)(x) is equal to

If f (x) =sin x+cos x, x in (-oo, oo) and g (x) = x^(2), x in (-oo,oo) then (fog)(x) is equal to

The function f(x) = max. {(1-x), (1+x), 2}, x in (-oo, oo) is

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4

Let f(x) lt 0 AA x in (-=oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=o, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt AA x in (-1,oo) also f '(-1)=0 given lim _(x to oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equatin f (x)=x ^(2) is :

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt AA x in (-1,oo) also f '(-1)=0 given lim _(x to oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. The minimum number of points where f'(x) is zero is: