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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS2 Marks
Question
If $f : R → R$ is defined by $f(x) = x^2 - 3x + 2$, write f{f(x)}.
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Answer

We have, $f(x)=x^2-3 x+2$
$\therefore f\{f(x)\}=f\left(x^2-3 x+2\right)$
$=\left(x^2-3 x+2\right)^2-3\left(x^2-3 x+2\right)+2$
$=x^4+9 x^2+4-6 x^3-12 x+4 x^2-3 x^2+9 x-6+2$
$=x^4-6 x^3+10 x^2-3 x$
$\therefore f\{f(x)\}=x^4-6 x^3+10 x^2-3 x$

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