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

Question Number 155809 by zainaltanjung last updated on 05/Oct/21

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

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

Answered by PRITHWISH SEN 2 last updated on 05/Oct/21

put t = \frac{x}{x - 2}

x = \frac{2}{t - 1} + 2 = \frac{2 t}{t - 1}

f (t) = \frac{{(\frac{2 t}{t - 1})}^{2}}{2 {(\frac{2 t}{t - 1})}^{2} - \frac{2 t}{t - 1} + 4}

= \frac{{4 t}^{2}}{{10 t}^{2} - 6 t + 4}

∴ f (x) = \frac{{4 x}^{2}}{{10 x}^{2} - 6 x + 4}