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  • Given the function f(x) = 1/x+2 Find the point of discontinuity of the composite function y = (f(x)).

Given the function  f(x)=\frac{1}{x+2}.  Find the point of discontinuity of the composite function y = f(f(x)).   

Answers (1)

Given,

F(x)=\frac{1}{x+2}

we have to find: Points discontinuity of composite function f(f(x))


As f(x) is not defined at x = -2 as denominator becomes 0, at x = -2.


\therefore x = -2 is a point of discontinuity

\because f(f(x))=f\left(\frac{1}{x+2}\right)=\frac{1}{\frac{1}{x+2}+2}=\frac{x+2}{2 x+5}

And f(f(x)) is not defined at x = -5/2 as denominator becomes 0, at x = -5/2.

∴ x = -5/2 is another point of discontinuity

Thus f (f(x)) has 2 points of discontinuity at x = -2 and x = -5/2

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infoexpert21

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