Let `A = R - {3}`and `B = R - {1}`. Consider the function `f: A->B`defined by `(x)=((x-2)/(x-3))`. Is f one-one and onto? Justify your answer.

Explanation

To determine whether the function \( f: A \to B \) defined by \( f(x) = \frac{x - 2}{x - 3} \) is one-one and onto, we will follow these steps:

### Step 1: Check if the function is one-one
To check if \( f \) is one-one, we need to show that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

Assume \( f(x_1) = f(x_2) \):
\[
\frac{x_1 - 2}{x_1 - 3} = \frac{x_2 - 2}{x_2 - 3}
...