Given-f-R-R-and-g-R-R-where-f-x-x-3-3-and-g-x-2x-1-Find-the-value-of-f-1-g-1-23-

Question Number 118960 by bramlexs22 last updated on 21/Oct/20

G i v e n f : R \to R a n d g : R \to R

w h e r e f (x) = x^{3} + 3 a n d g (x) = 2 x + 1 . F i n d

t h e v a l u e o f f^{- 1} (g^{- 1} (23)) .

Answered by benjo_mathlover last updated on 21/Oct/20

l e t f^{- 1} (g^{- 1} (23)) = q

t h e n g^{- 1} (23) = f (q) o r g (f (q)) = 23

g (q^{3} + 3) = 23 \Rightarrow 2 (q^{3} + 3) + 1 = 23

2 q^{3} + 7 = 23, q = \sqrt[3]{8} = 2 .

H e n c e f^{- 1} (g^{- 1} (23)) = 2