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 simplify. the difference quotient is □.

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Accepted Answer

# 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 $h
eq0$, we can factor out $h$ from the numerator and cancel it with the denominator: $\frac{h(2x + h)}{h}=2x+h$.
# Answer:
$2x + h$

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QUESTION IMAGE

Question

Explanation:

Step1: Find f(x + h)

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

Step3: Compute the difference - quotient

Answer: