Let f be an invertible function. Show that the inverse of `f^-1` is `f`

Let f:X rarr Y be an invertible function.Show that the inverse of is f,i.e.,(f^(-1))^(-1)=f

Let f: X->Y be an invertible function. Show that f has unique inverse. (Hint: suppose g_1(" and g")_2 are two inverses of f. Then for all y in Y ,""""fog_1(y)=I_Y(y)=fog_2(y) Use one oneness of f ).

Let f be an invertible real function. Write (f^(-1)\ of)(1)+(f^(-1)\ of)(2)++(f^(-1)\ of)(100)dot

Let f be an invertible function defined from R+ to R+t such that f(2)=5 and f^(-1)(x+4)=2f^(-1)(x)+1

Let f(x)=e^(x^(3)-x^(2)+x) be an invertible function such that f^(-1)=g ,then-

Statement-1 : Let f : [1, oo) rarr [1, oo) be a function such that f(x) = x^(x) then the function is an invertible function. Statement-2 : The bijective functions are always invertible .

Let f (x) be invertible function and let f ^(-1) (x) be is inverse. Let equation f (f ^(-1) (x)) =f ^(-1)(x) has two real roots alpha and beta (with in domain of f(x)), then :