Pertanyaan

Jika dan P − 1 adalah invers dari P, maka P − 2 = ...

Jika dan $P^{- 1}$ adalah invers dari P, maka $P^{- 2}$ = ...

A. Acfreelance

Master Teacher

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Pembahasan

$P equals open parentheses table row cell 1 plus x end cell x row cell negative x end cell cell 1 minus x end cell end table close parentheses P to the power of negative 1 end exponent equals fraction numerator 1 over denominator open parentheses 1 plus x close parentheses open parentheses 1 minus x close parentheses minus left parenthesis negative x squared right parenthesis end fraction open parentheses table row cell 1 plus x end cell x row cell negative x end cell cell 1 minus x end cell end table close parentheses P to the power of negative 1 end exponent equals fraction numerator 1 over denominator open parentheses 1 minus x squared close parentheses plus x squared end fraction open parentheses table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close parentheses P to the power of negative 1 end exponent equals open parentheses table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close parentheses P to the power of negative 2 end exponent equals open parentheses P to the power of negative 1 end exponent close parentheses squared space space space space space space space space equals P to the power of negative 1 end exponent. P to the power of negative 1 end exponent space space space space space space space space equals open parentheses table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close parentheses open parentheses table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close parentheses space space space space space space space space equals open parentheses table row cell open parentheses 1 minus x close parentheses squared minus x squared end cell cell negative x plus x squared minus x minus x squared end cell row cell x minus x squared plus x plus x squared end cell cell negative x squared plus open parentheses 1 plus x close parentheses squared end cell end table close parentheses space space space space space space space equals open parentheses table row cell 1 minus 2 x plus x squared minus x squared end cell cell negative 2 x end cell row x cell negative x squared plus 1 plus 2 x plus x squared end cell end table close parentheses space space space space space space equals open parentheses table row cell 1 minus 2 x end cell cell negative 2 x end cell row cell 2 x end cell cell 1 plus 2 x end cell end table close parentheses$

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