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1.) Let \(f\) be defined by

 

                               \(f(x) = \left\{ \begin{array}{cl} 3-x & \text{ if } x \leq 3, \\ -x^3+2x^2+3x & \text{ if } x>3. \end{array} \right.\)

 

Calculate \(f^{-1}(0)+f^{-1}(6).\)

 

 

 

2.) If \(f(x)=\frac{x+4}{x^2+ax+b},\) and \(f(x)\) has two vertical asymptotes at \(x=1\) and \(x=-2\), then find the sum of a and b.

 Aug 21, 2020
 #1
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1. f^{-1}(0) + f^{-1}(6) = 1 + (-2) = -1.

 

2. a + b = (-3) + (-2) = -5.

 Aug 21, 2020

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