Question

25 POINTS

What is the value of f(4) + g(3)? Two functions are shown. f(x) = 64(0.5) * Enter your response here: g(x) = 20x + 12 Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, .,-, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or a decimal.​

Answer 1

`\displaystyle f(4) + g(3) = 76`

Explanation:

We are given the two functions:

`\displaystyle f(x) = 64\left((1)/(2)\right)^x\text{ and } g(x)=20x+12`

And we want to find the value of:

`f(4)+g(3)`

We can find the value of each function individually.

Find f(4):

`\displaystyle \begin{aligned} f(4) & = 64\left((1)/(2)\right)^((4)) \\ \\ & = 64\left((1^4)/(2^4)\right) \\ \\ & = 64\left((1)/(16)\right) \\ \\ & = 4\end{aligned}`

Find g(3):

`\displaystyle \begin{aligned} g(3) & = 20(3) + 12 \\ \\ & = (60) + 12 \\ \\ & = 72\end{aligned}`

Therefore, substitute:

`\displaystyle \begin{aligned} f(4) + g(3) & = (4) + (72) \\ \\ & = 76\end{aligned}`

Therefore, in conclusion:

`\displaystyle f(4) + g(3) = 76`