Let-a-function-F-R-R-be-defined-by-f-x-1-ax-0-for-all-X-R-Show-that-f-is-invertible-and-find-its-inverse-function-Also-find-the-value-s-of-if-inverse-of-f-is-itself-

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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