Question 79

If $$f(x) = \frac{1}{1+x}$$, then find the value of $$f[f[f(x)]]$$, at x=5

Solution

$$f(x) = \frac{1}{1+x}$$

$$f[f(x)]$$ = $$\frac{1}{1+f(x)}$$ = $$\frac{1}{1+\frac{1}{1+x}}$$= $$\frac{1+x}{2+x}$$

$$f[f[f(x)]]$$ = $$\frac{1}{1+f{f(x)}}$$=$$\frac{1}{1+\frac{1+x}{2+x}}$$=$$\frac{2+x}{3+2x}$$

$$f[f[f(x)]]$$=$$\frac{2+5}{3+2*5}$$= $$\frac{7}{13}$$

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