CAT 2022 Slot 3 Paper

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Question : 59 of 66

Marks: +1, -0

Let $r$ be a real number and $f(x) = { 2x-r}/{r}$ if ${x≥ṛ}/{x

$x > r$
$x ≤ r$
$x ≠ r$
$x≥ r$

Solution:

When

x< r

f(x)=r

f(x)=f(f(x))

r=f(r)

r=2 r-r

r=r

When

x>=r

f(x)=2 x-r

f(x)=f(f(x))

2 x-r=f(2 x-r)

2 x-r=2(2 x-r)-r

2 x-r=4 x-3 r

or,

x=r

Therefore

x< =r

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