1. \(f^{-1} (x) = \cfrac{1}{2}x – \cfrac{1}{2}\)

   

2. \(g^{-1} (x) = \sqrt{ x + 1 }\)

   

3. \(h^{-1} (x) = \sqrt[3]{ x – 2 }\)

   

4. \(k^{-1} (x) = \cfrac{1}{x + 1}\)

   

5. \(f^{-1} (x) = 8 – \cfrac{x^2}{2}\)

   

6. \(g^{-1} (x) = \cfrac{ -7x – 15 }{ 3x – 5 }\)

   

In exercises 1 through 6, find and graph the inverse.

1. \[ f(x) = 2x+1 \]
2. \[ g(x) = x^2-1, \; x \geq 0 \]
3. \[ h(x) = x^3 + 2 \]
4. \[ k(x) = \frac{1}{x} -1 \]
5. \[ f(x) = \sqrt{16-2x} \]
6. \[ g(x) = \frac{5x-15}{3x+7} \]

7. Formally prove that:

   1. If \(f\) is increasing, then \(f^{-1}\) is increasing.
   2. If \(f\) is decreasing, then \(f^{-1}\) is decreasing.