F 0 x -1-1- x if x -0- f 0 x -1- x if x - 0 - Also given that f n x - f 0 f n -1 x -If x -1- find f 1 x f 2 x f 3 x - f 6 x -A -9B- 1-17C- 7-18D 1-0

The correct option is B 1/17Option (b) is the correct answer. Check the video for the approach. ...

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Functions

f 0 x =1/1+ x...

Question

$f^{0} (x) = \frac{1}{1 + x}$ if x > 0, $f^{0} (x) = 1 + x$ if x $\leq$ 0. Also given that $f^{n} (x) = f^{0} (f^{n - 1} (x))$ .
If x=1, find $f^{1} (x) f^{2} (x) f^{3} (x) \dots f^{6} (x)$ .

\frac{1}{6}

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\frac{1}{17}

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\frac{1}{18}

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\frac{1}{9}

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Solution

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Similar questions

f_{0} (x) = \frac{x}{(x + 1)}

f_{n + 1} = f_{0} \circ f_{n} (x)

n = 0, 1, 2, \dots

f_{n} (x)

⟨ f_{0} (x), f_{1} (x), f_{2} (x), \dots ⟩

f_{0} (x) = 1, f_{1} (x) = x, {(\begin{matrix} f_{n} (x) \end{matrix})}^{2} - 1 = f_{n + 1} (x) f_{n - 1} (x)

n \geq 1

f_{n} (x)

x \in R, x \neq 0, x \neq 1

f_{0} (x) = \frac{1}{1 - x}

f_{n + 1} (x) = f_{0} (f_{n} (x)), n = 0, 1, 2, . . . .

f_{100} (3) + f_{1} (\frac{2}{3}) + f_{2} (\frac{3}{2})

f_{n - 1} (x) = ln (f_{n} (x)) \forall n \in N

f_{0} (x) = x - 1

\frac{d}{d x} (f_{n} (x))

f (x) = {\begin{matrix} x + 1, i f x \leq 1 5 - x^{2} i f x > 1 \end{matrix}, g (x) = {\begin{matrix} x i f x \leq 1 2 - x i f x > 1 \end{matrix}

g (f (x)) + 2 = 0

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