Answer:
[tex]f^{-1}(x)=\sqrt[]{\frac{x-1}{3}}[/tex]Explanation:
Given the function:
[tex]f(x)=3x^2+1[/tex]To find the inverse function, follow the steps below:
Step 1: Replace f(x) with y
[tex]y=3x^2+1[/tex]Step 2: Swap x and y.
[tex]x=3y^2+1[/tex]Step 3: Make y the subject:
[tex]\begin{gathered} 3y^2=x-1 \\ y^2=\frac{x-1}{3} \\ y=\sqrt[]{\frac{x-1}{3}} \end{gathered}[/tex]Step 4: Replace y with the inverse function.
[tex]f^{-1}(x)=\sqrt[]{\frac{x-1}{3}}[/tex]