\( m(x)=x^{2}+4 x \) \[ n(x)=x \] \( (m n)(x)= \) \( x^{2}+4 x(x) \) \( \left(x^{2}+4 x\right)(x) \) DONE

To find \((m \cdot n)(x)\), we first need to substitute \(n(x)\) into \(m(x)\). Since \(n(x) = x\), we have: \[ (m \cdot n)(x) = m(n(x)) = m(x) \] Substituting \(n(x)\) into \(m(x)\): \[ m(n(x)) = m(x) = x^2 + 4x \] Thus, \((m \cdot n)(x) = x^2 + 4x\). Now, let's break down what it means. When you multiply functions like this, you're composing them, and here what's interesting is that you are not really combining functions; you are just reproducing \(m(x)\) because \(n(x)\) is identity. So, the final answer stays simply as \(x^2 + 4x\).