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Given the function f(x)=1/(x+2) . Find ...

Given the function `f(x)=1/(x+2)` . Find the points of discontinuity of the function `f(f(x))`

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The correct Answer is:
N/a
We have `f(x) = (1)/(x+2)`
`:. y = f{f(x)}`
` = f((1)/(x+2)) = (1)/((1)/(x+2)+2)`
`= (1)/(1+2x+4).(x+2)= ((x+2))/((2x+5))`
So, the function y will not continous at those points, where it is not denfined as it is a rational function.
Therefore, `y = (x+2)/((2x+5))` is not defined , when `2x + 5 = 0`
`:. x = (-5)/(2)`
Hence, y is discountinuous at `x = (-5)/(2)`
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