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Algebra
Pregunta

A formula for a function \( y = f ( x ) \) is \( f...

A formula for a function \( y = f ( x ) \) is \( f ( x ) = x ^ { 2 } - 16 x , x \leq 8 \) . Find \( f ^ { - 1 } ( x ) \) and identify the domain and range of \( f ^ { - 1 } ( x ) \) . To check the answer, determine whether 

\( f ( f ^ { - 1 } ( x ) ) = f ^ { - 1 } ( f ( x ) ) = x \) . (Hint: Complete the square.) \(f ^ { - 1 } ( x ) = \square \) 

(Type an exact answer, using radicals as needed.) The domain of \( f ^ { - 1 } ( x ) \) is \( \square \) 

(Type your answer in interval notation.) The range of \( f ^ { - 1 } ( x ) \) is \( \square \) . (Type your answer in interval notation.) Is \( f ( f ^ { - 1 } ( x ) ) = f ^ { - 1 } ( f ( x ) ) = x ? \) 

Yes No 

Answer

\(f^{- 1} (x)= 8- \sqrt{x+ 64}\)            

 domain    \((x\ge - 64)\)

range    : \((- \infty ,+ 8]\)

yes

Solución
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