Question

assume that the function f is a one - to - one function.
(a) if f(4)=7, find f^(-1)(7).
your answer is
(b) if f^(-1)(-2)=-4, find f(-4).
your answer is

Explanation:

Step1: Recall inverse - function property

For a one - to - one function \(y = f(x)\) and its inverse \(y = f^{-1}(x)\), if \(f(a)=b\), then \(f^{-1}(b)=a\), and if \(f^{-1}(c)=d\), then \(f(d)=c\).

Step2: Solve part (a)

Given \(f(4) = 7\), by the property of inverse functions, \(f^{-1}(7)=4\).

Step3: Solve part (b)

Given \(f^{-1}(-2)=-4\), by the property of inverse functions, \(f(-4)=-2\).

Answer:

(a) 4
(b) -2