Answer:
[tex]f^{-1}(x)=\sqrt[3]{\frac{1}{7}(x-2)}[/tex]
Step-by-step explanation:
The given equation is [tex]y=7x^3+2[/tex]
For finding inverse of this function, we apply below steps:-
Step 1
Interchange x and y
[tex]x=7y^3+2[/tex]
Step 2
Solve the equation for y
For this, subtract 2 to both sides of the equation
[tex]x-2=7y^3[/tex]
Divide both sides by 7
[tex]y^3=\frac{1}{7}(x-2)[/tex]
Take cube root both sides,
[tex]y=\sqrt[3]{\frac{1}{7}(x-2)}[/tex]
Step 3
Replace y with [tex]f^{-1}(x)[/tex]
Therefore, the inverse function is
[tex]f^{-1}(x)=\sqrt[3]{\frac{1}{7}(x-2)}[/tex]
