Given-that-fog-x-2x-1-x-and-g-x-5x-2-Find-f-x-

Question Number 142052 by Rankut last updated on 26/May/21

Given that fog (x) = \frac{2 x - 1}{x} and g (x) = 5 x + 2,

Find f (x) .

Answered by iloveisrael last updated on 26/May/21

\Rightarrow f (5 x + 2) = \frac{2 x - 1}{x}

\Rightarrow f (5 x + 2) = 2 - \frac{1}{x}

\Rightarrow f (x) = 2 - \frac{1}{(\frac{x - 2}{5})} = 2 - \frac{5}{x - 2}

\Rightarrow f (x) = \frac{2 x - 9}{x - 2}

Commented by Rankut last updated on 26/May/21

h o w d i d y o u g e t (\frac{x - 2}{5})

Answered by EDWIN88 last updated on 26/May/21

f (g (x)) = f (5 x + 2) = \frac{2 x - 1}{x}

let 5 x + 2 = u \Rightarrow x = \frac{u - 2}{5}

we get f (u) = \frac{2 (\frac{u - 2}{5}) - 1}{(\frac{u - 2}{5})} = \frac{2 u - 4 - 5}{u - 2}

f (u) = \frac{2 u - 9}{u - 2} \Rightarrow so f (x) = \frac{2 x - 9}{x - 2}

Answered by mathmax by abdo last updated on 26/May/21

fog (x) = \frac{2 x - 1}{5} \Rightarrow f (g (x)) = \frac{2 x - 1}{5} \Rightarrow f (5 x + 2) = \frac{2 x - 1}{x}

let 5 x + 2 = t \Rightarrow x = \frac{t - 2}{5} \Rightarrow f (t) = 2 - \frac{1}{\frac{t - 2}{5}} = 2 - \frac{5}{t - 2} = \frac{2 t - 4 - 5}{t - 2}

= \frac{2 t - 9}{t - 2} \Rightarrow f (x) = \frac{2 x - 9}{x - 2}