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प्रश्न
Given the function f(x) = `1/(x + 2)`. Find the points of discontinuity of the composite function y = f(f(x))
उत्तर
f(x) = `1/(x + 2)`
f[f(x)] = `1/("f"(x) + 2)`
= `1/(1/(x + 2) + 2)`
= `1/((1 + 2x + 4)/(x + 2))`
= `(x + 2)/(2x + 5)`
∴ f[f(x)] = `(x + 2)/(2x + 5)`
This function will not be defined and continuous where 2x + 5 = 0
⇒ x = `(-5)/2`.
Hence, x = `(-5)/2` is the point of discontinuity.
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