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### Question

### Hint:

For the given function we have to find the value of x when f(x) will be greater than or equals to 0. The given function has three cases we will put the value of x from each case and then determine when would f(x) will be 0 or positive.

#### The correct answer is:

#### For, , we have to find x when f(x) will be greater than or equals to 0.

As per the given function,

f(x) will be negative when

f(x) will be positive or 0 when (as f(x)= )

f(x) will be positive when (as f(x)= )

So, for

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#### Let

For

f(g(x))=f(1+x-)

f(g(2009))= f (1+2009-)

= f (1+2009-2009)

= f (1)

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f(g(x))=f(1+x-)

f(g(2009))= f (1+2009-)

= f (1+2009-2009)

= f (1)

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= g(1) (f(2009)=0 as x is greater than 0)

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For

f(g(x))=f(1+x-)

f(g(2009))= f (1+2009-)

= f (1+2009-2009)

= f (1)

=1 (as x is greater than 0)

g(f(x))=g(f(2009))

= g(1) (f(2009)=0 as x is greater than 0)

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f(g(x))=f(1+x-)

f(g(2009))= f (1+2009-)

= f (1+2009-2009)

= f (1)

=1 (as x is greater than 0)

g(f(x))=g(f(2009))

= g(1) (f(2009)=0 as x is greater than 0)

=1+1-

=2+1

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