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  • If f: R \rightarrow R is defined by f (x) = x\textsuperscript{2} - 3x + 2, write f (f (x)).\\

If  f:R \rightarrow R  is defined by f (x) = x\textsuperscript{2} - 3x + 2, write f (f (x)).

Answers (1)

Here, f (x) = x\textsuperscript{2} - 3x + 2

Therefore,

\\ f(f(x)) = f(x\textsuperscript{2} - 3x + 2)\\ = (x\textsuperscript{2} - 3x + 2)\textsuperscript{2} - 3(x\textsuperscript{2} - 3x + 2) + 2,\\ = x\textsuperscript{4} + 9x\textsuperscript{2} + 4 - 6x\textsuperscript{3} + 4x\textsuperscript{2} - 12x - 3x\textsuperscript{2} + 9x - 6 + 2\\ = x\textsuperscript{4} - 6x\textsuperscript{3} + 10x\textsuperscript{2} - 3x\\

Similarly,

\\f(f(x)) = x\textsuperscript{4} - 6x\textsuperscript{3} + 10x\textsuperscript{2} - 3x\\

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infoexpert22

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