f-x-1-x-and-g-x-x-2-2x-1-Find-g-1-f-3-

Question Number 179436 by Shrinava last updated on 29/Oct/22

f (x) = \frac{1}{x} and g (x) = \frac{x + 2}{2 x + 1}

Find : g^{- 1} (f (3)) = ?

Commented by cherokeesay last updated on 29/Oct/22

y = \frac{x + 2}{2 x + 1} \Leftrightarrow 2 x y + y = x + 2 \Rightarrow

x (2 y - 1) = 2 - y \Leftrightarrow x = \frac{2 - y}{2 y - 1}

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

g^{- 1} [f (3)] = \frac{2 - \frac{1}{3}}{2 \times \frac{1}{3} - 1} = - 5

Answered by ARUNG_Brandon_MBU last updated on 29/Oct/22

Let y = \frac{x + 2}{2 x + 1} \Rightarrow x = \frac{2 - y}{2 y - 1} \Rightarrow g^{- 1} (x) = \frac{2 - x}{2 x - 1}

f (3) = \frac{1}{3} \Rightarrow g^{- 1} (f (3)) = g^{- 1} (\frac{1}{3}) = - 5

Answered by mr W last updated on 29/Oct/22

f (3) = \frac{1}{3}

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

\Rightarrow x = - 5

g (- 5) = \frac{1}{3} = f (3)

\Rightarrow g^{- 1} (f (3)) = - 5

Commented by Shrinava last updated on 29/Oct/22

thank you dear professors