Question

this is section 2.8 problem 12: find the functions f(u) and g(x) for y = ln(3x^2 + 1), so that y = f(u) and u = g(x): f(u)= g(x)= hint: the variable in the first answer is u. resources ebook

Explanation:

Step1: Identify outer - inner functions

We know that the function $y = \ln(3x^{2}+1)$ is a composition of two functions. The outer - most function is the natural logarithm function and the inner function is the polynomial function inside the logarithm.

Step2: Define $f(u)$ and $g(x)$

Let $u = 3x^{2}+1$. Then $y=\ln(u)$. So, $f(u)=\ln(u)$ and $g(x)=3x^{2}+1$.

Answer:

$f(u)=\ln(u)$
$g(x)=3x^{2}+1$