Given-that-f-g-x-2-2x-2-x-4-and-g-x-x-x-2-find-f-x-

Question Number 152799 by nadovic last updated on 01/Sep/21

Given that f \circ g = \frac{x^{2}}{2 x^{2} - x + 4} and

g (x) = \frac{x}{x - 2}, find f (x) .

Commented by otchereabdullai@gmail.com last updated on 08/Sep/21

nice!

Answered by Olaf_Thorendsen last updated on 01/Sep/21

g (x) = \frac{x}{x - 2} = y

\Rightarrow x = \frac{2 y}{y - 1}

f o g (x) = \frac{x^{2}}{2 x^{2} - x + 4}

f o g (x) = \frac{\frac{4 y^{2}}{{(y - 1)}^{2}}}{\frac{8 y^{2}}{{(y - 1)}^{2}} - \frac{2 y}{y - 1} + 4}

f o g (x) = \frac{4 y^{2}}{8 y^{2} - 2 y (y - 1) + 4 {(y - 1)}^{2}}

f o g (x) = \frac{4 y^{2}}{8 y^{2} - 2 y^{2} + 2 y + 4 y^{2} - 8 y + 4}

f o g (x) = \frac{2 y^{2}}{5 y^{2} - 3 y + 2}

f (x) = \frac{2 x^{2}}{5 x^{2} - 3 x + 2}

Commented by SANOGO last updated on 01/Sep/21

v o u s e t e s g e n i a l e

Commented by puissant last updated on 01/Sep/21

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Commented by peter frank last updated on 03/Sep/21

good