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Question

If f : R → R is defined by f ( x ) = x 2 − 3 x + 2, find f ( f ( x )).

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Solution

It is given that the function f:RR is defined as f( x )= x 2 3x+2.

The value of function f( f( x ) ) is,

f( f( x ) )=f( x 2 3x+2 ) = ( x 2 3x+2 ) 2 3( x 2 3x+2 )+2 = x 4 +9 x 2 +46 x 3 12x+4 x 2 3 x 2 +9x6+2 = x 4 6 x 3 +10 x 2 3x

Thus, the value of f( f( x ) ) is x 4 6 x 3 +10 x 2 3x.


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