Answer:
inverse: [tex]f^{-1}(x) = \sqrt[5]{x^3 - 5}[/tex]
explanation:
Given: f(x) = [tex](x^5 +5)^{\frac{1}{3} }[/tex]
let f(x) be y
y = [tex](x^5 +5)^{\frac{1}{3} }[/tex]
To find inverse, make x the subject.
[tex]y^3 = x^5 + 5[/tex]
[tex]y^3 - 5 = x^5[/tex]
[tex]x = \sqrt[5]{y^3 - 5}[/tex]
change signs:
[tex]f^{-1}(x) = \sqrt[5]{x^3 - 5}[/tex]
