# Functions and more functions

**Calculus**Level pending

Let us define 2 functions \(f(x)\) and \(g(x)\) such that

\(f ^{\prime \prime} (x) = - f(x)\) and,

\(g(x) = f^{ \prime }(x)\)

Now lets define a new function \(H(x)\) such that

\(H(x) = \left( f \left(\dfrac x2\right) \right)^2 + \left( g\left(\dfrac x2\right) \right)^2\)

It is given that \(H(e) = \pi\). Then find value of \(H(\pi)\) upto 2 decimal places

**Notation**:

\(f ^{\prime} (x)\) refers to \(\displaystyle \frac{df(x)}{dx}\).

- \(f ^{\prime \prime} (x)\) refers to \(\displaystyle \frac{d^2f(x)}{dx^2}\).

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