Answer
$ a.\quad f$ is one-to-one
$b.\quad f^{-1}(x)=\displaystyle \frac{5x-2}{3}$
Work Step by Step
$f(x)=\displaystyle \frac{3x+2}{5}=\frac{3}{5}x+\frac{2}{5}$
$ a.\quad$
The function is linear, non-constant.
Its graph is an oblique line that passes the horizontal line test
(It is impossible to draw a horizontal line that intersects a function's graph more than once.)
It is one-to-one and has an inverse.
$ b.\quad$
To find a formula for the inverse,
1. Replace $f(x)$ with $y.$
$y=\displaystyle \frac{3x+2}{5}$
2. Interchange $x$ and $y$. (This gives the inverse function.)
$x=\displaystyle \frac{3y+2}{5}$
3. Solve for $y.$
... multiply with $5$,
$ 5x=3y+2\qquad$... subtract $2$,
$ 5x-2=3y\qquad$...divide with $3$
$\displaystyle \frac{5x-2}{3}=y$
4. Replace $y$ with $f^{-1}(x)$ . (This is inverse function notation.)
$f^{-1}(x)=\displaystyle \frac{5x-2}{3}$
