Answer
$f(x)=g(x)$
Work Step by Step
a. For graph, please see image attached.
b.
For algebraic verification, we use Th.5.2.
Property $1$ : $\ln(1)=0$
Property $2$ : $\ln(ab)=\ln a + \ln b$
Property $3$ : $\ln(a^{n})=n\cdot\ln a $
Property 4 : $\displaystyle \ln(\frac{a}{b})=\ln a - \ln b$
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$f(x)=\ln\sqrt{x(x^{2}+1)}=\ln[x(x^{2}+1)]^{1/2}$= ... property $3$...
$=\displaystyle \frac{1}{2}\cdot\ln[x(x^{2}+1)]$= ... property $2$...
$=\displaystyle \frac{1}{2}\cdot[\ln x+\ln(x^{2}+1)]$=$ g(x)$
