$$f(x) = \frac{x-5}{x+5}, x \neq -5$$, then the obtained of $$f^{-1}(x)$$ is—

Explanation

$$f(x) = y = \frac{x-5}{x+5}$$ Swap x and y— $$x = \frac{y-5}{y+5}$$ $$x(y+5) = y-5$$ ## Page 46 $$xy + 5x = y - 5$$ $$xy - y = -5x - 5$$ $$y(x - 1) = -5x - 5$$ $$y = \frac{5(x + 1)}{1 - x}$$ so $f^{-1}(x) = \frac{5(x + 1)}{(1 - x)}$ Clearly $x \neq 1$ So, obtained = R – {1} In the question, letters are coded using some special symbols/ numbers. RAIN → 8 $ % 6 MORE → 7 # 8 @ According to the code obtained above: R → 8, E → @, M → 7, A → $, I → %, N → 6 Therefore, the code for REMAIN will be: 8 @ 7 $ % 6.