`f(x)={c^x ,0lt=x1 2-c^(x-1),1

Find the greatest and least values of function f(x)={-x , -1lt=x<0 2-(x-1)^2, 0lt=xlt=2

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

Discuss the continuity of the function f(x)={x , 0lt=x<1//2 12 , x=1//2 1-x , 1//2

f(x)={(4, xlt-1) ,(-4x,-1lt=xlt=0):} If f(x) is an even function in R then the definition of f(x) in (0,oo) is: (A) f(x)={(4x, 0ltxle1),(4, xgt1):} (B) f(x)={(4x, 0ltxle1),(-4, xgt1):} (C) f(x)={(4, 0ltxle1),(4x, xgt1):} (D) f(x)={(4, xlt-1),(-4x, -1lexle0):}

If f(x)={(x^2)/2 , if 0lt=xlt=1 2x^2-3x+3/2 , if 1

Let f(x)={1+(2x)/a ,0lt=x<1 and ax ,1lt=x<2 If lim_(x->1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

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

f(x)={(log_(e)x",",0lt x lt 1),(x^(2)-1 ",",x ge 1):} and g(x)={(x+1",",x lt 2),(x^(2)-1 ",",x ge 2):} . Then find g(f(x)).

Let f(x)={{:(,3^x,at,-1lt x lt0),(,4,at,0 le x lt 1),(,3x-1, at,1 le x le 3):} Find f(2), f(0), f(0.5), f(-0.5), f(3).

Let f(x)={{:(,x^(3),x lt 1),(,ax^(2)+bx+c,:x ge 1):} . If f''(1) exists, then the value of (a^(2)+b^(2)+c^(2)) is