Let `f(x)=x^3-3x^2+6AAx in R` and `g(x)={m a x :f(t ; x+1lt=tlt=x+2,-3lt=xlt=0 1-x ,xgeq`

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

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........ .

Let f(x)=[|x|-|x-1|]^(2) What is f'(x) equal to when 0lt xlt1 ?

If f(x)=m a xi mu m{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,0lt=xlt=1x^3,x >0 f(x)={1/(64),0lt=xlt=1/4x^2,1/4 1 f(x)={1/(64),0lt=xlt=1/8x^2,1/8 1 f(x)={1/(64),0lt=xlt=1/8x^3,x >1/8

Find the values of aa n db so that the function f(x) defined by f(x)={x^2+a x+b,0lt=x<2 3x+2,2lt=xlt=42a x+5b ,4

Let f(x)=x^(3)+x be function and g(x)={(f(|x|)",", x ge 0),(f(-|x|)",",x lt 0):} , then

If f: R->R : x!=0,\ -4lt=xlt=4 and f: A->A be defined by f(x)=(|x|)/x for x in A . Then A is {1,-1} b. {x :0lt=xlt=4} c. {1} d. {x :-4lt=xlt=0}

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is