Answer:
The inverse of the function is [tex]f^{-1}(x) =\sqrt[5]{\frac{x-7}{3}}[/tex]
Step-by-step explanation:
The steps to get the inverse of a function are:
∵ [tex]f(x)=3x^{5}+7[/tex]
- Replace f(x) by y
∴ [tex]y=3x^{5}+7[/tex]
- Replace every x by y and every y by x
∴ [tex]x=3y^{5}+7[/tex]
- Subtract 7 from both sides
∴ [tex]x-7=3y^{5}[/tex]
- Divide both sides by 3
∴ [tex]\frac{x-7}{3}=y^{5}[/tex]
- Insert fifth root for both sides
∴ [tex]\sqrt[5]{\frac{x-7}{3}}=y[/tex]
- Switch the two sides
∴ [tex]y=\sqrt[5]{\frac{x-7}{3}}[/tex]
- replace y by [tex]f^{-1}(x)[/tex]
∴ [tex]f^{-1}(x) =\sqrt[5]{\frac{x-7}{3}}[/tex]
The inverse of the function is [tex]f^{-1}(x) =\sqrt[5]{\frac{x-7}{3}}[/tex]
