I have an Advanced Professional Certificate (APC I) in Mathematics 7-12, from the state of Maryland. I teach Physics, AP Physics, and Genetics & Forensics on the HS level. I also teach college algebra at the university level.
For the following exercises, determine the domain for each function in interval notation.Given $f(x)=-3 x^{2}+x$ and $g(x)=5,$ find $f+g$ $f-g, f g$ , and $\frac{f}{g}$
For the following exercises, determine the domain for each function in interval notation.Given $f(x)=\frac{1}{x-4}$ and $g(x)=\frac{1}{6-x},$ find $f+g, f-g, f g,$ and $\frac{f}{g}$
For the following exercises, determine the domain for each function in interval notation.Given $f(x)=\sqrt{x}$ and $g(x)=|x-3|,$ find $\frac{g}{f}$
For the following exercises, use each pair of functions to find $f(g(x))$ and $g(f(x)) .$ Simplify your answers.$$f(x)=x^{2}+1, g(x)=\sqrt{x+2}$$
For the following exercises, use each pair of functions to find $f(g(x))$ and $g(f(x)) .$ Simplify your answers.$$f(x)=|x|, g(x)=5 x+1$$
For the following exercises, use each pair of functions to find $f(g(x))$ and $g(f(x)) .$ Simplify your answers.$$f(x)=\frac{1}{x-6}, g(x)=\frac{7}{x}+6$$