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Question
Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]
Solution
We know that f(x) = `1/(x - 1)` is discontinuous at x = 1
Now, for x ≠ 1,
f(f(x)) = `"f"(1/(x - 1))`
= `1/(1/(x - 1) - 1)`
= `(x - 1)/(2 - x)`.
Which is discontinuous at x = 2.
Hence, the points of discontinuity are x = 1 and x = 2.
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