Let $$ P(s) $$ be the function $$ \frac{s}{s+1}-1 $$. Find the following: $$ P(11)=-\frac{1}{12} $$ $$ P(-4)= $$ $$ P\left(\frac{1}{8}\right)= $$ $$ P\left(-\frac{1}{3}\right)=\square $$ In each box, enter your answer as an integer or reduced fraction. Enter DNE for Does Not Exist, or oo for Infinity.

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UpStudy AI · Accepted Answer

1. For $$ P(-4) $$:
   $$
   P(-4)=\frac{-4}{-4+1}-1=\frac{-4}{-3}-1=\frac{4}{3}-1=\frac{4-3}{3}=\frac{1}{3}
   $$

2. For $$ P\left(\frac{1}{8}\right) $$:
   $$
   P\left(\frac{1}{8}\right)=\frac{\frac{1}{8}}{\frac{1}{8}+1}-1=\frac{\frac{1}{8}}{\frac{9}{8}}-1=\frac{1}{9}-1=\frac{1-9}{9}=\frac{-8}{9}
   $$

3. For $$ P\left(-\frac{1}{3}\right) $$:
   $$
   P\left(-\frac{1}{3}\right)=\frac{-\frac{1}{3}}{-\frac{1}{3}+1}-1=\frac{-\frac{1}{3}}{\frac{2}{3}}-1=-\frac{1}{3}\times\frac{3}{2}-1=-\frac{1}{2}-1=-\frac{3}{2}
   $$

Thus, the answers are:
- $$ P(-4)=\frac{1}{3} $$
- $$ P\left(\frac{1}{8}\right)=-\frac{8}{9} $$
- $$ P\left(-\frac{1}{3}\right)=-\frac{3}{2} $$
$$ P(-4) = \frac{1}{3} $$, $$ P\left(\frac{1}{8}\right) = -\frac{8}{9} $$, $$ P\left(-\frac{1}{3}\right) = -\frac{3}{2} $$

Let be the function . Find the following:

In each box, enter your answer as an integer or reduced fraction. Enter DNE for Does Not Exist, or oo for
Infinity.

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Let be the function . Find the following: In each box, enter your answer as an integer or reduced fraction. Enter DNE for Does Not Exist, or oo for Infinity.