Show that `f(x)=5x-4` , `0< x < 1` `f(x)=4x^3-3x` , `1< x <2` continuous at `x=1`

Explanation

To show that the function \( f(x) \) is continuous at \( x = 1 \), we need to verify that the left-hand limit and the right-hand limit at \( x = 1 \) are equal, and that they equal the function value at that point.

### Step 1: Define the function pieces
The function is defined as:
- \( f(x) = 5x - 4 \) for \( 0 < x < 1 \)
- \( f(x) = 4x^3 - 3x \) for \( 1 < x < 2 \)

### Step 2: Calculate the left-hand limit as \( x \) approaches 1
...