Home
Class 12
MATHS
Let f: X -> Y be an invertible function...

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

Text Solution

Verified by Experts

We are given,
`f:X->Y ` is an invertible function.
Let `g: Y->X` be the inverse of `f`, `:. g = f^-1`
so, `fog = I_X and gof = I_Y`
Let `g^-1` be the inverse of `g`.
Then, `g^-1og = I_X and gog^-1 = I_Y`
`=>f^-1of = I_X and fof^-1 = I_Y`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f be an invertible function.Show that the inverse of f^(-1) is 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(x)=e^(x^(3)-x^(2)+x) be an invertible function such that f^(-1)=g ,then-

Let f : R rarr R : f(x) = (2x-3)/(4) be an invertible function. Find f^(-1) .

Let f : R to R : f(x) =(2x-7)/(4) be an invertible function . Find f^(-1)

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 :

Let f:A rarr B be an invertible function.If f(x)=2x^(3)+3x^(2)+x-1, then f^(-1)(5)=

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

Let f: R->R be defined by f(x)=3x-7 . Show that f is invertible and hence find f^(-1) .