Suppose that the functions f and g are defined as follows, {:[f(x)=x+2],[g(x)=sqrt(3x+4)]:} Find (f)/(g) and f+g. Then, give their domains using interval notation.

Define f and g functions: Define the functions f and g: f(x) = x + 2, g(x) = sqrt(3x + 4).Calculate (f/g)(x): Calculate (f/g)(x): (f/g)(x) = (x + 2) / sqrt(3x + 4).Calculate (f+g)(x): Calculate (f+g)(x): (f+g)(x) = (x + 2) + sqrt(3x + 4).Determine domain of g(x): Determine the domain of g(x): sqrt(3x + 4) is defined for 3x + 4 >= 0. Solve 3x + 4 >= 0, 3x >= -4, x >= -4/3. Domain of g(x): x >= -4/3.Determine domain of f(x): Determine the domain of f(x): f(x) = x + 2 is defined for all real x. Domain of f(x): all real numbers.Find common domain: Find the common domain for (f/g)(x) and (f+g)(x): Since g(x) has a more restrictive domain, the common domain is x >= -4/3.

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Suppose that the functions $f$ and $g$ are defined as follows, $\begin{cases} f(x) = x + 2 \ g(x) = \sqrt{3x + 4} \end{cases}$ Find $\frac{f}{g}$ and $f + g$ . Then, give their domains using interval notation.

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Algebra 1

Domain and range of square root functions: equations

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Q. Suppose that the functions

f

and

g

are defined as follows,

\begin{cases} f(x) = x + 2 \ g(x) = \sqrt{3x + 4} \end{cases}

Find

\frac{f}{g}

and

f + g

. Then, give their domains using interval notation.

Define f and g functions: Define the functions f and g: $\newline$ f(x) = $x + 2$ , $\newline$ g(x) = $\sqrt{3x + 4}$ .
Calculate $(f/g)(x)$ : Calculate $(f/g)(x)$ : $(f/g)(x) = \frac{x + 2}{\sqrt{3x + 4}}$ .
Calculate $(f+g)(x)$ : Calculate $(f+g)(x)$ : $(f+g)(x) = (x + 2) + \sqrt{3x + 4}$ .
Determine domain of $g(x)$ : Determine the domain of $g(x)$ : $\sqrt{3x + 4}$ is defined for $3x + 4 \geq 0$ . Solve $3x + 4 \geq 0$ , $3x \geq -4$ , $x \geq -\frac{4}{3}$ . Domain of $g(x)$ : $x \geq -\frac{4}{3}$ .
Determine domain of $f(x)$ : Determine the domain of $f(x)$ : $f(x) = x + 2$ is defined for all real $x$ . $\newline$ Domain of $f(x)$ : all real numbers.
Find common domain: Find the common domain for $(f/g)(x)$ and $(f+g)(x)$ : $\newline$ Since $g(x)$ has a more restrictive domain, the common domain is $x \geq -\frac{4}{3}$ .