Answer:
[tex]f^{-1}(x) = \sqrt[5]{\frac{x+7}{9} -10}[/tex]
Explanation:
given : f(x) = 9( [tex]x^5[/tex] + 10 ) - 7
replace x and y with each other.
- x = 9( [tex]y^5[/tex] + 10 ) - 7
solve for y
- x + 7 = 9( [tex]y^5[/tex] + 10 )
- ( [tex]y^5[/tex] + 10 ) = [tex]\frac{x + 7}{9}[/tex]
- [tex]y^5[/tex] + 10 = [tex]\frac{x + 7}{9}[/tex]
- [tex]y^5[/tex] = [tex]\frac{x + 7}{9}[/tex] - 10
- y = [tex]\sqrt[5]{\frac{x+7}{9} -10}[/tex]
Therefore,
- [tex]f^{-1}(x) = \sqrt[5]{\frac{x+7}{9} -10}[/tex]
