Problem

Source:

Tags: function, quadratics, algebra proposed, algebra



Is it possible that by using the following transformations: \[ f(x) \mapsto x^2 \cdot f \left(\frac{1}{x}+1 \right) \ \ \ \text{or} \ \ \ f(x) \mapsto (x-1)^2 \cdot f\left(\frac{1}{x-1} \right)\] the function $f(x)=x^2+5x+4$ is sent to the function $g(x)=x^2+10x+8$ ?