If `f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot`

If f(x)=(e^(x)+e^(-x))/(2) then inverse of f(x) is

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

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-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)= ______ for x>20

If f:[0,oo[rarr R is the function defined by f(x)=(e^(z^(2))-e^(-x^(2)))/(e^(x^(2))-e^(-x^(2))), then check whether f(x) is injective or not.

If f: RvecR is a differentiable function such that f^(prime)(x)>2f(x)fora l lxRa n df(0)=1,t h e n : f(x) is decreasing in (0,oo) f^(prime)(x) e^(2x)in(0,oo)

If f(x)=int_(0)^(x)tf(t)dt+2, then