Question

Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x2Find H(x+ a)- H(x)/a

Answer 1

If H(x) is x^2

Then, H(x+a) is calculated replacing x by (x+a) as:

`\begin{gathered} H(x+a)=(x+a)^2=x^2+2ax+a^2 \\ H(x)=x^2 \end{gathered}`

So, (H(x+ a) - H(x) )/a is equal to:

`\begin{gathered} (H(x+a)-H(x))/(a)=(x^2+2ax+a^2-x^2)/(a) \\ (H(x+a)-H(x))/(a)=(2ax+a^2)/(a) \\ (H(x+a)-H(x))/(a)=2x+a \end{gathered}`

Answer: (H(x+ a) - H(x) )/a = 2x + a