Solutions
Solutions to Try Its
1. [latex]{f}^{-1}\left(f\left(x\right)\right)={f}^{-1}\left(\frac{x+5}{3}\right)=3\left(\frac{x+5}{3}\right)-5=\left(x - 5\right)+5=x\\[/latex] and [latex]f\left({f}^{-1}\left(x\right)\right)=f\left(3x - 5\right)=\frac{\left(3x - 5\right)+5}{3}=\frac{3x}{3}=x\\[/latex] 2. [latex]{f}^{-1}\left(x\right)={x}^{3}-4\\[/latex] 3. [latex]{f}^{-1}\left(x\right)=\sqrt{x - 1}\\[/latex] 4. [latex]{f}^{-1}\left(x\right)=\frac{{x}^{2}-3}{2},x\ge 0\\[/latex] 5. [latex]{f}^{-1}\left(x\right)=\frac{2x+3}{x - 1}\\[/latex]Solutions to Odd-Numbered Exercises
1. It can be too difficult or impossible to solve for x in terms of y. 3. We will need a restriction on the domain of the answer. 5. [latex]{f}^{-1}\left(x\right)=\sqrt{x}+4\\[/latex] 7. [latex]{f}^{-1}\left(x\right)=\sqrt{x+3}-1\\[/latex] 9. [latex]{f}^{-1}\left(x\right)=-\sqrt{\frac{x - 5}{3}}\\[/latex] 11. [latex]f\left(x\right)=\sqrt{9-x}\\[/latex] 13. [latex]{f}^{-1}\left(x\right)=\sqrt[3]{x - 5}\\[/latex] 15. [latex]{f}^{-1}\left(x\right)=\sqrt[3]{4-x}\\[/latex] 17. [latex]{f}^{-1}\left(x\right)=\frac{{x}^{2}-1}{2},\left[0,\infty \right)\\[/latex] 19. [latex]{f}^{-1}\left(x\right)=\frac{{\left(x - 9\right)}^{2}+4}{4},\left[9,\infty \right)\\[/latex] 21. [latex]{f}^{-1}\left(x\right)={\left(\frac{x - 9}{2}\right)}^{3}\\[/latex] 23. [latex]{f}^{-1}\left(x\right)={\frac{2 - 8x}{x}}\\[/latex] 25. [latex]{f}^{-1}\left(x\right)=\frac{7x - 3}{1-x}\\[/latex] 27. [latex]{f}^{-1}\left(x\right)=\frac{5x - 4}{4x+3}\\[/latex] 29. [latex]{f}^{-1}\left(x\right)=\sqrt{x+1}-1\\[/latex] 31. [latex]{f}^{-1}\left(x\right)=\sqrt{x+6}+3\\[/latex] 33. [latex]{f}^{-1}\left(x\right)=\sqrt{4-x}\\[/latex]









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