Cook Bolton
01/18/2024 · Senior High School
\( \operatorname { IUn } [ 22 ^ { 4 } ] = \frac { 4 ^ { 2 } + 1 - ( z ^ { 2 } + 1 ) } { z } \)
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Para resolver la expresión dada, primero necesitamos simplificar la expresión dentro del índice de la función inversa.
Dado que \( \operatorname { IUn } [ 22 ^ { 4 } ] \) representa la función inversa de \( 22 ^ { 4} \), podemos simplificar \( 22 ^ { 4} \) como \( 22 \times 22 \times 22 \times 22 \).
Entonces, la expresión se convierte en:
\[ \operatorname { IUn } [ 22 ^ { 4 } ] = \frac { 4 ^ { 2 } + 1 - ( z ^ { 2 } + 1 ) } { z } \]
Simplificando \( 22 ^ { 4} \) y sustituyendo en la expresión, obtenemos:
\[ \operatorname { IUn } [ 22 ^ { 4 } ] = \frac { 4 ^ { 2 } + 1 - ( z ^ { 2 } + 1 ) } { z } = \frac { 16 + 1 - ( z ^ { 2 } + 1 ) } { z } = \frac { 17 - z ^ { 2 } } { z } \]
Por lo tanto, la expresión simplificada es \( \frac { 17 - z ^ { 2 } } { z } \).
Quick Answer
La expresión simplificada es \( \frac { 17 - z ^ { 2 } } { z } \).
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