Unit 4 Investigation

Explain why this conclusion is valid: $t(d(100))=84.80,$ while $d(t(100))=86$. Use the foundation problem as evidence: Coupon $d(p)=p-20$ and tax $t(q)=1.06q$ at $p=100$.

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Create a nearby example by changing one number or condition in this prompt: $f=\frac{1}{x},g=x-4$; domain. Predict the effect, solve your new example, and compare it with the original.

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Create a nearby example by changing one number or condition in this prompt: Domain $ln(4-x^2)$. Predict the effect, solve your new example, and compare it with the original.

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Create a nearby example by changing one number or condition in this prompt: Inverse of $\frac{x+3}{2}$. Predict the effect, solve your new example, and compare it with the original.

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Correct this reasoning and identify the first unsafe assumption: A frequent error is replacing $sqrt(x^2)$ with $x$ for negative inputs or omitting the final check.

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