`A={1, 0},f i n dAxxAxxA`

If f is an odd continuous function in [-1,1] and differentiable in (-1,1) then a. f'(A)=f(1)" for some "A in (-1,0) b. f'(B) =f(1)" for some "B in (0,1) c. n(f(A))^(n-1)f'(A)=(f(1))^(n)" for some " A in (-1, 0), n in N d. n(f(B))^(n-1)f'(B)=(f(1))^(n)" for some" B in (0,1), n in N

Let f((x+y)/2)=(f(x)+f(y))/2fora l lr e a lxa n dy If f^(prime)(0) exists and equals -1a n df(0)=1,t h e n f i n d f(2)dot

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ e v e nn-1,\ if\ n\ i s\ od d Show that f is a bijection.

Let f: Nuu{0}->Nuu{0} be defined by f={(n+1 ,, ifn \ i s \ e v e n),(n-1 ,, ifn \ i s \ od d):} Show that f is a bijection.

Let f: N uu {0} rarr N uu {0} be defined by : f(n)= {(n+1, if n is even),(n-1, if n is odd):} .Show that f is invertible and f =f^-1 .

For non-negative integers m and n a function is defined as follows: f(m,n)={n+1, if m=0 and f(m-1,1) if m!=0,n=0 and f(m-1,f(m,n-1)) if m!=0,n Then the value of f(1,1) is:

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .