Question

Still confusing to me!!!!

Answer 1

Answer:

  (a)  2(x -a)

  (b)  4x +2h

Step-by-step explanation:

Fill in the function arguments and simplify.

a.

$\dfrac{f(x)-f(a)}{x-a}=\dfrac{(2x^2-7)-(2a^2-7)}{x-a}\\\\=\dfrac{2x^2-7-2a^2+7}{x-a}=\dfrac{2(x^2-a^2)}{x-a}\\\\=\dfrac{2(x-a)(x+a)}{(x-a)}=2(x+a)$

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b.

$\dfrac{f(x+h)-f(x)}{h}=\dfrac{(2(x+h)^2-7)-(2x^2-7)}{h}\\\\=\dfrac{2x^2+4xh+2h^2-7-2x^2+7}{h}=\dfrac{4xh+2h^2}{h}\\\\=4x+2h$