" 02.If "f(x)={[3*-1,," for "-1<=x<0],[tin(x/2),," for "0<=x<=pi," then "sqrt(f(0)+f(pi/6)+(1)/(5)f(5)-(1)/(23))=],[(x)/(x^(2)-2)," for "x<=x<=6]

A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(3-ax^(2),"for " xgt1):} If f (x) is continuous at x = 1 , find the value of a.

If f(x)=3^(-x)-1 , for -1 le x lt0, =tan(x//2), " for "0lexltpi =(x)/(x^(2)-2)," for "pilexlt6, then f(-1)+f(pi//6)+f(5)=

Examine the continuity of f(x)={((|x-3|)/(x-1)" , "xne3),(1" , "x=3):} at x=3.

If f(x)=(1)/(3x+1)," then: "f'(0)

The function defined by f(x)={x^(3)-1;1

If f(x)={(3x-1),x>=1,(2x+3),x =2} then lim_(x rarr2)f(g(x))=

If f(x)=(x-1)/(2x^(2)-7x+5) for x!=1 and f(x)=-(1)/(3) for x=1 then f'(1)=

If f from R into R defined by f(x)=x^(3)-1, then f^(-1){-2, 0, 7}=