Chapter 2.6, Problem 30E

(a)

To determine

To evaluate: The functions $\left(f+g\right)\left(x\right)$, $\left(f-g\right)\left(x\right)$, and $\left(f\cdot g\right)\left(x\right)$ for $f\left(x\right)=\sqrt{2+4x^2}$ and $g\left(x\right)=x$.

(b)

To determine

To find: The domain of the functions $\left(f+g\right)\left(x\right)$, $\left(f-g\right)\left(x\right)$, and $\left(f\cdot g\right)\left(x\right)$ where $f\left(x\right)=\sqrt{2+4x^2}$ and $g\left(x\right)=x$.

(c)

To determine

To evaluate: The function $\left(\frac{f}{g}\right)\left(x\right)$ where $f\left(x\right)=\sqrt{2+4x^2}$ and $g\left(x\right)=x$ and give its domain.

(d)

To determine

To find: The value of the composition $\left(f\circ g\right)\left(x\right)$ for the functions $f\left(x\right)=\sqrt{2+4x^2}$ and $g\left(x\right)=x$ and give the domain.

(e)

To determine

To find: The value of the composition $\left(g\circ f\right)\left(x\right)$ for the functions $f\left(x\right)=\sqrt{2+4x^2}$ and $g\left(x\right)=x$ and then give the domain.