Answer:
[tex]g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}[/tex]
Step-by-step explanation:
The inverse of a function has [tex]x[/tex] and [tex]y[/tex] values switched from the original function. Therefore, simply switch [tex]x[/tex] and [tex]y[/tex] and isolate [tex]y[/tex] to get your inverse function:
Original function: [tex]g(x)=41x^3+a[/tex]
Switching [tex]x[/tex] and [tex]y[/tex], then isolating [tex]y[/tex]:
[tex]x=41y^3+a,\\x-a=41y^3,\\\frac{x-a}{41}=y^3,\\y=\sqrt[3]{\frac{x-a}{41}}[/tex].
Therefore, the inverse of the [tex]g(x)=41x^3+a[/tex] is:
[tex]\fbox{$g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}$}[/tex].
