Given-g-x-x-11-x-1-x-1-If-f-x-8-f-g-x-15-x-find-the-value-of-f-13-

Question Number 134506 by bemath last updated on 04/Mar/21

Given g (x) = \frac{x + 11}{x - 1}; x \neq 1

If f (x) + 8 (f \circ g) (x) = 15 - x, find

the value of f (13) .

Answered by EDWIN88 last updated on 04/Mar/21

first step, we must find the value of {\begin{cases} g (2) \\ g (13) \end{cases}

\Leftrightarrow {\begin{cases} g (2) = \frac{13}{1} = 13 \\ g (13) = \frac{24}{12} = 2 \end{cases}

second step

put x = 2 \Rightarrow f (2) + 8 f (g (2)) = 13

f (2) + 8 f (13) = 13 \dots (i)

put x = 13 \Rightarrow f (13) + 8 f (g (13)) = 2

f (13) + 8 f (2) = 2 \dots (ii)

8 \times (i) - (ii) \Rightarrow 63 f (13) = 102

f (13) = \frac{102}{63} \approx 1.62

Answered by Ñï= last updated on 04/Mar/21

f (13) + 8 f (g (13)) = 15 - 13 = 2

g (13) = \frac{24}{12} = 2

1) :: f (13) + 8 f (2) = 2

f (2) + 8 f (g (2)) = 15 - 2 = 13

g (2) = 13

2) :: f (2) + 8 f (13) = 13

1) \land 2)

\Rightarrow f (13) = \frac{34}{21}

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