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Jika f ( x ) = a x , g ( x ) = f ( x ) + f ( − x ) , dan h ( x ) = f ( x ) − f ( − x ) , maka ( g ( x ) ) 2 − ( h ( x ) ) 2 = ....

Jika , , dan , maka  ....

  1. -4

  2. -2

  3. 0

  4. 2

  5. 4

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Pembahasan

Karena , maka dan Maka

Karena undefined , maka

begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals straight f left parenthesis straight x right parenthesis plus straight f left parenthesis negative straight x right parenthesis equals straight a to the power of straight x plus straight a to the power of negative straight x end exponent end style 

dan

begin mathsize 14px style straight h left parenthesis straight x right parenthesis equals straight f left parenthesis straight x right parenthesis minus straight f left parenthesis negative straight x right parenthesis equals straight a to the power of straight x minus straight a to the power of negative straight x end exponent end style 

Maka

begin mathsize 14px style left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis squared minus left parenthesis straight h left parenthesis straight x right parenthesis right parenthesis squared equals left parenthesis straight a to the power of straight x plus straight a to the power of negative straight x end exponent right parenthesis squared minus left parenthesis straight a to the power of straight x minus straight a to the power of negative straight x end exponent right parenthesis squared equals left parenthesis left parenthesis straight a to the power of straight x right parenthesis squared plus 2 times straight a to the power of straight x times straight a to the power of negative straight x end exponent plus left parenthesis straight a to the power of negative straight x end exponent right parenthesis squared right parenthesis minus left parenthesis left parenthesis straight a to the power of straight x right parenthesis squared minus 2 times straight a to the power of straight x times straight a to the power of negative straight x end exponent plus left parenthesis straight a to the power of negative straight x end exponent right parenthesis squared right parenthesis equals left parenthesis straight a squared straight x plus 2 plus straight a to the power of negative 2 straight x end exponent right parenthesis minus left parenthesis straight a squared straight x minus 2 plus straight a to the power of negative 2 straight x end exponent right parenthesis equals straight a squared straight x plus 2 plus straight a to the power of negative 2 straight x end exponent minus straight a squared straight x plus 2 minus straight a to the power of negative 2 straight x end exponent equals 4 end style 

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