The brightness of a spotlight at a point on a stage
MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions
Problem
The brightness I(d) of a spotlight at a point on a stage, measured in arbitrary units, is modelled by
I(d)=d2−25100,
where d (in metres) is the horizontal distance of the point from the centre of the light.
(i) Find all real values of d for which the expression I(d) is undefined.
(ii) The stage extends only in the interval 0≤d≤20. Taking this physical restriction into account, state the distances on the stage that must be avoided because the brightness model is invalid there.
(iii) Write the domain of I(d), restricted to 0≤d≤20, in interval notation.