Question

A one-to-one function is given. Write an expression for the inverse function.

Answer 1

We have to find the inverse function for m, defined as:

$m(x)=7x^3+2$

If g(x) is the inverse of m(x), we can define:

$m[g(x)]=x$

This means that if we use the inverse function as argument of m(x) we will obtain the input of g(x), that is x.

We can use it to find the expression of g(x) as:

$\begin{gathered} m(g(x))=x \\ 7g(x)^3+2=x \\ 7g(x)^3=x-2 \\ g(x)^3=\frac{x-2}{7} \\ \\ g(x)=\sqrt[3]{\frac{x-2}{7}} \end{gathered}$

As g(x) is m^-1(x), we can express it as:

$m^{-1}(x)=\sqrt[3]{\frac{x-2}{7}}$

Answer: m^-1(x) = ∛[(x-2)/7]

[Option b]