Prove that the function `f: R->R` defined as `f(x)=2x+3` is invertible. Also, find `f^(-1)` .

Explanation

To prove that the function \( f: \mathbb{R} \to \mathbb{R} \) defined as \( f(x) = 2x + 3 \) is invertible, we need to show that it is both one-to-one (injective) and onto (surjective). Then, we will find the inverse function \( f^{-1} \).

### Step 1: Prove that \( f \) is one-to-one (injective)

To show that \( f \) is one-to-one, we assume that \( f(x_1) = f(x_2) \) for some \( x_1, x_2 \in \mathbb{R} \).

\[
f(x_1) = f(x_2) \implies 2x_1 + 3 = 2x_2 + 3
...