Question

$Find space straight f left parenthesis straight A right parenthesis space comma space given space straight f left parenthesis straight X right parenthesis space equals space straight x squared minus 7 straight x minus 2 space and space straight A equals space open square brackets table row cell 2 space space end cell 3 row 4 5 end table close square brackets$

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Solution

Here space straight f left parenthesis straight x right parenthesis equals straight x squared minus 7 straight x minus 2 therefore space space space space space straight f left parenthesis straight A right parenthesis space equals straight A squared space space minus 7 straight A minus 2 space straight I space space space space space space space space space space space straight A space equals space open square brackets table row 2 cell space space 3 end cell row 4 cell space space 5 end cell end table close square brackets space space space space space space space space space space space space straight A squared space equals space open square brackets table row 2 cell space space 3 end cell row 4 cell space space 5 end cell end table close square brackets space space open square brackets table row 2 cell space space 3 end cell row 4 cell space space 5 end cell end table close square brackets space equals space open square brackets table row cell 4 plus 12 end cell cell space space 6 plus 15 end cell row cell 8 plus 20 end cell cell space space 12 plus 25 end cell end table close square brackets space space space equals space open square brackets table row 16 cell space 21 end cell row 28 cell space 37 end cell end table close square brackets space space space space space space space space straight f left parenthesis straight A right parenthesis space equals straight A squared space space minus 7 straight A minus 2 space straight I space space space space space space space space space space space space space space space space equals space open square brackets table row 16 cell space space 21 end cell row 28 cell space space 37 end cell end table close square brackets space minus 7 space open square brackets table row bold 2 cell bold space bold space bold 3 end cell row bold 4 cell bold space bold space bold 5 end cell end table close square brackets minus 2 space open square brackets table row bold 1 cell bold space bold 0 end cell row bold 0 cell bold space bold space bold 1 end cell end table close square brackets space space space space space space space space space space space space space space space space equals space open square brackets table row 16 cell space space 21 end cell row 28 cell space space 37 end cell end table close square brackets plus open square brackets table row cell negative 14 end cell cell negative 21 end cell row cell negative 28 end cell cell negative 35 end cell end table close square brackets plus space open square brackets table row cell negative 2 end cell cell bold space bold 0 end cell row bold 0 cell bold space bold space bold minus bold 2 end cell end table close square brackets space space space space space space space space space space space space space space space equals space open square brackets table row cell 16 minus 14 minus 2 end cell cell space space 21 minus 21 plus 0 end cell row cell 28 minus 28 plus 0 space end cell cell space space 37 minus 35 minus 2 end cell end table close square brackets equals space open square brackets table row 0 cell space space 0 end cell row 0 cell space space 0 end cell end table close square brackets therefore space space space space space space space space space space space straight f left parenthesis straight A right parenthesis equals straight O

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