Let and . If the range of this function is , then the value of is…

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

f: \mathbb{R} \to \mathbb{R}

and

f(x) = \frac{3x^2 + mx + n}{x^2 + 1}

. If the range of this function is

[-4, 3]

, then the value of

\frac{m^2 + n^2}{4}

is .....