If `f(x)={x-2,xlt=0 4-x^2,x >0,t h e nd i s c u s st h econ t inu i t yof` `y=f(f(x))dot`

Let f(x)={-x^2,forx<0x^2+8,forxgeq0t h e nx-in t e r c e p toft h e line, that is, the tangent to the graph of f(x) , is zero (b) -1 (c) -2 (d) -4

Show that f(x)={(x-|x|)/(2),2 w h e nx!=0i sd i s con t inuou sa tx=0dotw h e nx=0

I fx+1/x=2,t h e p r i n c i p a l v a l u e o f sin^(-1)x is

If f(x)={x-1,xgeq1 2x^2-2,x 0-x^2+1,xlt=0,a n dh(x) =|x|,t h e n("lim")_(xvec0)f(g(h(x))) is___

If f(x)=x^(2)-2|x|, then test the continuity and differentiability of g(x) in the interval [-2,3], where g(x)=min{f(t):2<=t<=x},-2<=x<0 and max{f(t):0<=t<=x,0<=x<=

Statement 1: If g(x) is a differentiable function, g(2)!=0,g(-2)!=0, and Rolles theorem is not applicable to f(x)=(x^2-4)/(g(x))in[-2,2],t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b),t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b), then Rolles theorem is applicable for x in (a , b)dot

[ Let f and g be two real valued functions and S={x|f(x)=0} and T={x|g(x)=0}, then S nn T represent the set of roots of [ (a) f(x)g(x)=0, (b) f(x)^(2)+g(x)^(2)=0 (c) f(x)+g(x)=0, (d) (f(x))/(g(x))=0]]

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=