Question

Find the domain of f(x)^-1 if f(x)= -9x-3

Answer 1

We have
\[f(x)=-9x-3\]
Let's find \(f^{-1} (x)\) first
we know that
\[f(f^{-1} (x))=x\]
let's replace \(x\) by \(f^{-1} (x)\) in f(x)
we get
\[f(f^{-1} (x))=-9f^{-1} (x) -3\]
\[x=-9f^{-1} (x) -3\]
so
\[f^{-1}(x)=-\frac{(x+3)}{9}\]
there is no value of x for which \(f^{-1} (x)\) is undefined
so domain is all real numbers