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Consider the function f(x)= {{:((x+5)/(x...

Consider the function f(x)= `{{:((x+5)/(x-2),"if " xne 2),(" 1", "if " x=2):}` . Then f(f(x)) is discontinuous

A

at all real numbers

B

at excatly two values of x

C

at ecactly one value of x

D

at exactly three values of x

Text Solution

Verified by Experts

The correct Answer is:
B
discontinuous at x=2
`f(f(x))=f((x+5)/(x-2))`
`(((x+5)/(x-2)+5))/(((x+5)/(x-2)-2))=(6x-5)/(-x+9)`
`(6x-5)/(9-x)`
At x=9 it is discontinuous
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