Consider the function f(x) = { \\begin{array}{c}{{x+5\end\frac{array}{x-2}}, \if x\neq2;1,\if x -2.} Then f ( f( x)) is discontinuous

Correct Answer is : at exactly two values of x

KVPY SX SB Exam 20141 Question Paper

Question : 9 of 120

Marks: +1, -0

Consider the function

f(x) = { \{\table {{x+5}/{x-2}}, \if x≠2;1,\if x -2.}

Then

f ( f( x))

is discontinuous

Solution:

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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