If f(x)=`[ 1+x^2 ; x<=1 ,x+1; 1< x<=2` and `g(x)=1-x ; -2<=x<=1` then define the function `fog(x)`

If f(x) = 1 + x + x^(2) + …… for |x| lt 1 then show that f^(-1)(x) = (x-1)/(x) .

If f(x) = 1-x + x^(2) - x^(3) + …. - x^(99) + x^(100) , then f^(')(1) is equal to

"I : If f(x) = cosh x + sinh x then "f(x_1 + x_2 "+...+" x_a)= f(x_1)*f(x_2)*** f(x_n) "II : If f(x) = cosh x + sinh x then "f(x_1) + f(x_2) "+...+"f(x_n) = f(x_1)* f(x_2) ***f(x_n)

If f(x)=1+x+x^(2)+x^(3)+...oo for |x|<1 then f^(-1)(x)=

If f(x)=1-x+x^2-x^3+......-x^(99)+x^(100) then f^(prime)(1) equals

If f(x)=1-x+x^(2)-x^(3)+ . . .-x^(99)+x^(100) then f'(1) is equal to

If f(x) + 2f(1 - x) = x^2 + 2, forall x in R , then f(x) is