given $f(x)=x^{2}-2x$,
(a) find $f(x + h)$ and simplify.
(b) find $\frac{f(x + h)-f(x)}{h}$ and simplify.
part: $0 / 2$
part 1 of 2
(a) $f(x + h)=\square$

Question

Accepted Answer

# Explanation:
## Step1: Substitute $x + h$ into $f(x)$
Given $f(x)=x^{2}-2x$, substitute $x=x + h$ into the function.
$$
\begin{align*}
f(x + h)&=(x + h)^{2}-2(x + h)\
\end{align*}
$$
## Step2: Expand $(x + h)^{2}$ and $2(x + h)$
Using the formula $(a + b)^{2}=a^{2}+2ab + b^{2}$ ($a = x$, $b = h$), $(x + h)^{2}=x^{2}+2xh+h^{2}$, and $2(x + h)=2x + 2h$.
$$
\begin{align*}
f(x + h)&=x^{2}+2xh + h^{2}-2x-2h
\end{align*}
$$

# Answer:
$f(x + h)=x^{2}+2xh + h^{2}-2x - 2h$

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QUESTION IMAGE

Question

Explanation:

Step1: Substitute \(x + h\) into \(f(x)\)

Step2: Expand \((x + h)^{2}\) and \(2(x + h)\)

Answer: