An object is 30.0 cm from a spherical mirror along the central axis. The absolute value of lateral magnification is `(1)/(2)`. The image produced is inverted. What is the focal length of the mirror?

Explanation

To solve the problem step by step, we will use the mirror formula and the magnification formula for spherical mirrors.

### Step 1: Identify the given values
- Object distance (u) = -30.0 cm (negative because the object is in front of the mirror)
- Lateral magnification (|m|) = 1/2
- Since the image is inverted, the magnification (m) will be negative: m = -1/2

### Step 2: Use the magnification formula
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