Given-the-functions-f-x-2x-1-and-f-g-x-x-2-x-2-find-g-x-

Question Number 43353 by pieroo last updated on 10/Sep/18

Given the functions f (x) = 2 x - 1 and f ∙ g (x) = x^{2} - x + 2,

find g (x)

Commented by maxmathsup by imad last updated on 10/Sep/18

w e h a v e f (x) = y \Rightarrow 2 x - 1 = y \Rightarrow x = \frac{y + 1}{2} \Rightarrow f^{- 1} (x) = \frac{x + 1}{2}

b u t f o g (x) = x^{2} - x + 2 \Rightarrow f^{- 1} o f o g (x) = f^{- 1} (x^{2} - x + 2) \Rightarrow

g (x) = f^{- 1} (x^{2} - x + 2) = \frac{x^{2} - x + 2 + 1}{2} = \frac{x^{2} - x + 3}{2} .

Answered by Joel578 last updated on 10/Sep/18

f (x) = 2 x - 1

f (g (x)) = x^{2} - x + 2

2 g (x) - 1 = x^{2} - x + 2

g (x) = \frac{x^{2} - x + 3}{2} = \frac{1}{2} x^{2} - \frac{1}{2} x + \frac{3}{2}

Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18

2 g (x) - 1 = x^{2} - x + 2

2 g (x) = x^{2} - x + 3

g (x) = \frac{x^{2} - x + 3}{2}