Question 2

Let $\mathbb{A} = \mathbb{R} - \{2\}$ and let $\mathbb{B} = \mathbb{R} - \{3\}$.
For $x \in \mathbb{A}$, let $${f(x) = \frac{3x -2}{x - 2}}$$.

• Prove that $f$ is a well-defined map from $\mathbb{A}$ to $\mathbb{B}$.
• Discuss, with proof, whether or not $f$ is invertible and if $f$ is invertible, obtain a formula for the inverse function.
• Determine, with proof, the direct image $f([4, \infty))$.