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
Imagine you have a machine that converts kilograms to pounds, represented by the function f ( x ) . The inverse function, h ( x ) , would convert pounds back to kilograms. If you input a weight in kilograms into f ( x ) to get pounds, and then input that result into h ( x ) , you would get back the original weight in kilograms. This concept is used in unit conversions, encoding/decoding messages, and many other applications where reversing a process is necessary.
