Mitchell Lindsey
12/03/2023 · Middle School
Given the function \( f(x)=-3-x^{2} \), express the value of \( \frac{f(x+h)-f(x)}{h} \) in simplest form.
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( -3-(x+h)^{2}+3+x^{2} \).
Simplify the expression by following steps:
- step0: Solution:
\(-3-\left(x+h\right)^{2}+3+x^{2}\)
- step1: Simplify:
\(-\left(x+h\right)^{2}+x^{2}\)
- step2: Expand the expression:
\(-x^{2}-2hx-h^{2}+x^{2}\)
- step3: Remove the opposites:
\(-2hx-h^{2}\)
The value of \( \frac{f(x+h)-f(x)}{h} \) in simplest form is \( -2x - h \).
Quick Answer
\( -2x - h \)
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