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QuestionFind (gf)(3)\left(\frac{g}{f}\right)(3) where g(a)=3a+2g(a)=3a+2 and f(a)=2a−4f(a)=2a-4.

Studdy Solution

STEP 1

Assumptions1. We have two functions, g(a)=3a+g(a) =3a + and f(a)=a−4f(a) =a -4. . We need to find the value of (gf)(3)\left(\frac{g}{f}\right)(3), which means we need to evaluate the function g(a)g(a) at a=3a =3, evaluate the function f(a)f(a) at a=3a =3, and then divide the result of g(3)g(3) by f(3)f(3).

STEP 2

First, we need to find the value of g(a)g(a) when a=a =. We can do this by substituting a=a = into the equation for g(a)g(a).
g()=()+2g() =() +2

STEP 3

Now, calculate the value of g(3)g(3).
g(3)=3(3)+2=9+2=11g(3) =3(3) +2 =9 +2 =11

STEP 4

Next, we need to find the value of f(a)f(a) when a=3a =3. We can do this by substituting a=3a =3 into the equation for f(a)f(a).
f(3)=2(3)−4f(3) =2(3) -4

STEP 5

Now, calculate the value of f(3)f(3).
f(3)=2(3)−4=−4=2f(3) =2(3) -4 = -4 =2

STEP 6

Now that we have the values of g(3)g(3) and f(3)f(3), we can find the value of (gf)(3)\left(\frac{g}{f}\right)(3) by dividing g(3)g(3) by f(3)f(3).
(gf)(3)=g(3)f(3)\left(\frac{g}{f}\right)(3) = \frac{g(3)}{f(3)}

STEP 7

Substitute the values of g(3)g(3) and f(3)f(3) into the equation.
(gf)(3)=112\left(\frac{g}{f}\right)(3) = \frac{11}{2}

STEP 8

Calculate the value of (gf)(3)\left(\frac{g}{f}\right)(3).
(gf)(3)=112=5.5\left(\frac{g}{f}\right)(3) = \frac{11}{2} =5.5So, (gf)(3)=5.5\left(\frac{g}{f}\right)(3) =5.5.

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