Discussion

Question:

Find the value of $f (f (\frac{1}{2}))$ + $f (f (f (3)))$ , if f(x) = $\{\begin{cases} \frac{1}{x - 1} & if x is an integer \\ \frac{1}{1 - x} & if x is not an integer \end{cases}$

Explanation:

f(1/2) = $\frac{1}{1 - 1 / 2}$ = 2
f(f(1/2)) = f(2) = $\frac{1}{2 - 1}$ = 1

Also,
f(3) = $\frac{1}{3 - 1}$ = $\frac{1}{2}$
f(f(3)) = f(1/2) = $\frac{1}{1 - 1 / 2}$ = 2
f(f(f(3))) = f(2) = $\frac{1}{2 - 1}$ = 1

∴ f(f(1/2)) + f(f(f(3))) = 1 + 1 = 2

Hence, option (a).

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