If H(x) is x^2
Then, H(x+a) is calculated replacing x by (x+a) as:
[tex]\begin{gathered} H(x+a)=(x+a)^2=x^2+2ax+a^2 \\ H(x)=x^2 \end{gathered}[/tex]So, (H(x+ a) - H(x) )/a is equal to:
[tex]\begin{gathered} \frac{H(x+a)-H(x)}{a}=\frac{x^2+2ax+a^2-x^2}{a} \\ \frac{H(x+a)-H(x)}{a}=\frac{2ax+a^2}{a} \\ \frac{H(x+a)-H(x)}{a}=2x+a \end{gathered}[/tex]Answer: (H(x+ a) - H(x) )/a = 2x + a
