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A convex mirror of radius of curvature $$30$$ cm forms an image that is half the size of the object. The object distance is :
$$R = +30\text{ cm} \implies f = \frac{R}{2} = +15\text{ cm}$$
$$m = -\frac{v}{u} = +\frac{1}{2} \implies v = -\frac{u}{2}$$
Mirror formula:
$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$
$$\frac{1}{15} = \frac{1}{\left(-\frac{u}{2}\right)} + \frac{1}{u} = -\frac{2}{u} + \frac{1}{u} = -\frac{1}{u}$$
$$u = -15\text{ cm}$$
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