Answer:
[tex]f^{-1} (x) = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }[/tex]
Step-by-step explanation:
Let f(x) = y
Interchange x and y so
[tex]x = \frac{1}{\sqrt{y^{3} + 9 } }[/tex]
[tex]x\sqrt{y^{3} + 9} = 1[/tex]
[tex]\sqrt{y^{3} + 9 } = \frac{1}{x}[/tex]
[tex]y^{3} + 9 = \frac{1}{x^{2} }[/tex]
[tex]y^{3} = \frac{1}{x^{2} } - 9[/tex] = [tex]\frac{1 - 9x^{2} }{x^{2} }[/tex]
[tex]y = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }[/tex]
[tex]f^{-1} (x) = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }[/tex]
