Let `f (x) =cos x, g (x)={{:(min {f (t):0 le t le x}",", x in[0","pi]),((sin x)-1"," , x gtpi):}` Then

Let f(x) = sin x and " g(x)" = {{:(max {f(t)","0 le x le pi},"for", 0 le x le pi),((1-cos x)/(2)",","for",x gt pi):} Then, g(x) is

Let f(x) = sin x and " g(x)" = {{:(max {f(t)","0 le x le pi},"for", 0 le x le pi),((1-cos x)/(2)",","for",x gt pi):} Then, g(x) is

Let f : [ 0, oo) to [ 0,3] be a function defined by f(x) = {{:(max { sin t : 0 le t le x}" , " 0 le x le pi),( 2 + cos x", " x gt pi ):} Then which of the following is true ?

Let f(x) = sin x and "c g(x)" = {{:(max {f(t)","0 le x le pi},"for", 0 le x le pi),((1-cos x)/(2)",","for",x gt pi):} Then, g(x) is

f(x) = cos x and H(x) = {{:(min{f(t), 0 le t lt x},0 le x le (pi)/(2)) ,( (pi)/(2)-x,(pi)/(2) lt x le 3):} then

Let f(x)=sin x and cg(x)={max{f(t),0 pi Then ,g(x) is

Let f(x) = -x^(3) + x^(2) - x + 1 and g(x) = {{:(min(f(t))",",0 le t le x and 0 le x le 1),(x - 1",",1 lt x le 2):} Then, the value of lim_(x rarr 1) g(g(x)) , is........ .

If f(x) = x^(2) - 2|x| and g(x) = {{:("min{f(t)":-2 le t le x",",-2 le x le "}"),("max {f(t):"0 le t le x",",0 le x le 3"}"):} (i) Draw the graph of f(x) and discuss its continuity and differentiablity. (ii) Find and draw the graph of g(x Also, discuss the continuity.

Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):} Then, g(x) in [0, 2] is