Question

Determine wheter the function is one-on-one. If it is, find a formula for its inverse.
f(x)=4/5x+a

Answer 1

is this
\[f(x)=\frac{4}{5x+a}\]?

Answer 2

if so, it is indeed one to one. you can find the inverse by writing \(x=\frac{4}{5y+a}\) and solving for \(y\)

Answer 3

\[x=\frac{4}{5y+a}\]
\[5xy+ax=4\]
\[5xy=4-ax\]
\[y=\frac{4-ax}{5x}\] and so
\[f^{-1}(x)=\frac{4-ax}{5x}\]