If $h(x)$ is the inverse of $f(x)$, what is the value of $h(f(x))$?
A. 0
B. 1
C. $x$
D. $f(x)$
Answer (1)
Recognize that h ( x ) is the inverse of f ( x ) .
Apply the definition of an inverse function: h ( f ( x )) = x .
Conclude that the value of h ( f ( x )) is x .
The final answer is x .
Explanation
Understanding the Problem The problem states that h ( x ) is the inverse of f ( x ) . We need to find the value of h ( f ( x )) .
Applying the Definition of Inverse Function By the definition of an inverse function, if h ( x ) is the inverse of f ( x ) , then h ( f ( x )) = x for all x in the domain of f .
Conclusion Therefore, h ( f ( x )) = x .
Examples
In cryptography, inverse functions are used for encoding and decoding messages. If f ( x ) is an encoding function and h ( x ) is the decoding function (the inverse of f ( x ) ), then applying f to a message x gives the encoded message f ( x ) , and applying h to the encoded message f ( x ) gives back the original message h ( f ( x )) = x . This ensures that the original message can be recovered accurately.
