be a function defined as 
The inverse of f is the map g : Range f 
given by(A) g(y) = (B) g(y) = (C) g(y) =
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be given by 
, then 
(x) is
be an invertible function. Show that the inverse of 
is f, i.e., 
given by f(1) = a, f(2) = b and f(3) = c. Find 
and show that 
.(Hint: suppose and are two inverses of f. Then for all
given by 
.Show that f is invertible with 
.
given by 
. Show that f is invertible with the inverse 
, where 
is the set of all non-negative real numbers.![f : [-1, 1] \to R](https://eduhilfe.com/wp-content/ql-cache/quicklatex.com-25c0d6d7d7dcc21db3b80220f182b0a2_l3.png "Rendered by QuickLaTeX.com")
, given by 
is one-one. Find the inverse of the function ![f : [-1, 1] \to \text{Range} f](https://eduhilfe.com/wp-content/ql-cache/quicklatex.com-143d6adbb0550db965689c66680ed29d_l3.png "Rendered by QuickLaTeX.com")
.( Hint : For y Range f, y = f(x) = , for ...
(i) f : {1, 2, 3, 4} {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)} (ii) g : {5, 6, 7, 8}