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Section 3.7 : Inverse Functions

1. Given \(P\left( x \right) = 12x - 7\) find \({P^{ - 1}}\left( x \right)\).
2. Given \(g\left( x \right) = 7x\) find \({g^{ - 1}}\left( x \right)\).
3. Given \(\displaystyle h\left( x \right) = \frac{3}{4} - \frac{9}{7}x\) find \({h^{ - 1}}\left( x \right)\).
4. Given \(A\left( x \right) = 4 - {\left( {x + 3} \right)^5}\) find \({A^{ - 1}}\left( x \right)\).
5. Given \(f\left( x \right) = 2{\left( {1 - 4x} \right)^3} + 1\) find \({f^{ - 1}}\left( x \right)\).
6. Given \(P\left( x \right) = \sqrt[7]{{5 - 8x}}\) find \({P^{ - 1}}\left( x \right)\).
7. Given \(g\left( x \right) = 1 + \sqrt[3]{{3x + 4}}\) find \({g^{ - 1}}\left( x \right)\).
8. Given \(\displaystyle f\left( x \right) = \frac{{10 - 3x}}{{8x}}\) find \({f^{ - 1}}\left( x \right)\).
9. Given \(\displaystyle g\left( x \right) = \frac{{6x - 7}}{{4 + x}}\) find \({g^{ - 1}}\left( x \right)\).
10. Given \(\displaystyle f\left( x \right) = \frac{{3 - x}}{{9 - 7x}}\) find \({f^{ - 1}}\left( x \right)\).