1.

If the functionf(x) = 1/(x+2),then find the points of discountinuity of the composite functiony = f{f(x)}.

Answer»


Solution :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 functiony will not continousat those points, whereit is not denfined as it is a RATIONALFUNCTION.
THEREFORE, `y = (x+2)/((2x+5))` is not defined, when `2x + 5 = 0`
`:.x = (-5)/(2)`
Hence,y isdiscountinuousat `x= (-5)/(2)`


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