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Chapter 2: Problem 88

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with the linear function \(f(x)=3 x+5\) and \(I\) do not need to find \(f^{-1}\) in order to determine the value of \(\left(f \circ f^{-1}\right)(17)\).

Short Answer

Expert verified
The statement makes sense. It's not necessary to find \(f^{-1}\) in order to determine the value of \(\left(f \circ f^{-1}\right)(17)\). This is because the composition of a function and its inverse always produces the original value, in this case, \(17\).

Step by step solution

01

Understand function composition

The composition of a function and its inverse, symbolized as \((f \circ f^{-1})(x)\), results in the original \(x\). In this specific case, \((f \circ f^{-1})(x)=x\) for all \(x\) in the domain of \(f^{-1}\), which means that \(\left(f \circ f^{-1}\right)(17) = 17\).
02

Apply the specific case

To get the value of \(\left(f \circ f^{-1}\right)(17)\), it's not necessary to find \(f^{-1}\). Simply substitute \(17\) into \(x\).

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