Question

for the given functions f and g, find the following. For parts (a)-(d), also find the domain. x=2x^2+3;g(x)=4x^3+1 for a (f+g)(x) and d (f/g)(x)

Answer 1

\[(f+g)(x)=f(x)+g(x)\] so our job is to put a plus sign between them and then combine like terms
you will get a polynomial, and domain will be all real numbers

Answer 2

similarly
\[\frac{f}{g}(x)=\frac{f(x)}{g(x)}\] so put f on top of g
you will get
\[\frac{f}{g}(x)=\frac{2x^2+3}{4x^3+1}\]

Answer 3

for this one the denominator cannot be zero, so to find the domain you must solve
\[4x^3+1\neq 0\]
\[4x^3\neq -1\]
\[x^3\neq -\frac{1}{4}\]
\[x\neq -\frac{1}{\sqrt[3]{4}}\]

Answer 4

ty