Questions: Let f(x)=x^2+3x and g(x)=4-x. Find (f/g)(x) and (f/g)(2). (f/g)(x)=(x^2+3x)/(4-x) (Simplify your answer.) (f/g)(2)= (Type an integer or fraction.)

$Let f(x)=x^2+3x and g(x)=4-x. Find (f/g)(x) and (f/g)(2). (f/g)(x)=(x^2+3x)/(4-x) (Simplify your answer.) (f/g)(2)= (Type an integer or fraction.)$

Transcript text: Let $f(x)=x^{2}+3 x$ and $g(x)=4-x$. Find $\left(\frac{f}{g}\right)(x)$ and $\left(\frac{f}{g}\right)(2)$. $\left(\frac{f}{g}\right)(x)=\frac{x^{2}+3 x}{4-x}$ (Simplify your answer.) $\left(\frac{f}{g}\right)(2)=\square$ (Type an integer or fraction.)

Solution

Solution Steps

Step 1: Define the functions $ f(x) $ and $ g(x) $

Given: \[ f(x) = x^{2} + 3x \] \[ g(x) = 4 - x \]

Step 2: Compute $\left(\frac{f}{g}\right)(x)$

The quotient of the functions $ f(x) $ and $ g(x) $ is: \[ \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{x^{2} + 3x}{4 - x} \]

Step 3: Compute $\left(\frac{f}{g}\right)(2)$

Substitute $ x = 2 $ into $\left(\frac{f}{g}\right)(x)$: \[ \left(\frac{f}{g}\right)(2) = \frac{(2)^{2} + 3(2)}{4 - 2} = \frac{4 + 6}{2} = \frac{10}{2} = 5 \]

Final Answer

\[ \boxed{\left(\frac{f}{g}\right)(2) = 5} \]

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