Let a function F :R→R be defined by f(x)=1+ax,α≠ 0 for all X ∈ R. Show that f is invertible and find its inverse function.Also find the value (s) of α if inverse of f is itself


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Question Number 32161 by jarjum last updated on 20/Mar/18

$L e t a f u n c t i o n F : R \to R b e d e f i n e d b y$ $f (x) = 1 + a x, α \neq 0 f o r a l l X \in R . S h o w$ $t h a t f i s i n v e r t i b l e a n d f i n d i t s i n v e r s e$ $f u n c t i o n . A l s o f i n d t h e v a l u e (s) o f α$ $i f i n v e r s e o f f i s i t s e l f$
	Answered by mrW2 last updated on 21/Mar/18

	$f (x) = 1 + a x$ $f^{- 1} (x) = \frac{x - 1}{a}$ $w i t h a = - 1 :$ $f^{- 1} (x) = f (x)$
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