Question

Find the inverse of the function.

f(x) = 6x3 + 3

Answer 1

so you find the inverse of a function by doing a quick "switcharoo" on the letters/variables

so if the function is

\(f(x) = 6x^3 + 3 \implies y = 6x^3 + 3\)

the inverse will be by switching it about

\(x = 6y^3 + 3 \)
and solve for "y" there
whatever you'd get, is the inverse function :)

Answer 2

To find the inverse of the function f we write :
\[f(y)=x\]
and then we try to find the y !

We have :
\[f(y)=x\iff 6y^3+3=x\\\iff 6y^3=x-3\\
\iff y^3=\frac{x-3}{6}
\iff y=\sqrt[3]{\frac{x-3}6}
\]
So the inverse function of f is the function :
\[f^{-1}(x)=\sqrt[3]{\frac{x-3}6}\]

Answer 3

thank you