find the difference quotient of f(x)=x^2 - 1; that is find $\frac{f(x + h)-f(x)}{h}$, h≠0. be sure to…

Explanation:

Step1: Find f(x + h)

Given (f(x)=x^{2}-1), then (f(x + h)=(x + h)^{2}-1=x^{2}+2xh+h^{2}-1).

Step2: Calculate f(x + h)-f(x)

[ \begin{align*} f(x + h)-f(x)&=(x^{2}+2xh + h^{2}-1)-(x^{2}-1)\ &=x^{2}+2xh+h^{2}-1 - x^{2}+1\ &=2xh+h^{2} \end{align*} ]

Step3: Compute the difference - quotient

(\frac{f(x + h)-f(x)}{h}=\frac{2xh + h^{2}}{h}). Since (h\neq0), we can factor out (h) from the numerator and cancel it with the denominator: (\frac{h(2x + h)}{h}=2x+h).

Answer:

(2x + h)