Question

homework assignment 1.7: inverse functions
score: 0/15 answered: 0/15
question 1
assume that the function f is a one - to - one function.
(a) if f(6) = 6, find $f^{-1}(6)$.
your answer is
(b) if $f^{-1}(-9) = -3$, find f(-3).
your answer is
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Explanation:

Part (a)

Step1: Recall inverse function property

For a one - to - one function \(f\), if \(f(a)=b\), then \(f^{-1}(b) = a\).
We are given that \(f(6)=6\). Comparing with \(f(a)=b\) (where \(a = 6\) and \(b = 6\)), by the property of inverse functions, \(f^{-1}(6)=6\).

Part (b)

Step1: Recall inverse function property

For a one - to - one function \(f\), if \(f^{-1}(b)=a\), then \(f(a)=b\).
We are given that \(f^{-1}(- 9)=-3\). Comparing with \(f^{-1}(b)=a\) (where \(b=-9\) and \(a = - 3\)), by the property of inverse functions, \(f(-3)=-9\).

Answer:

(a):
\(6\)