The carnival is arriving in the neighborhood! Leo has saved up $15 to spend at the carnival on food and attractions. Food items cost $4 each and attractions cost $2 each. Leo uses the expression 4a + 2b to determine the total cost for a food items and b attractions.

Question

Select one of the following combinations of food items and attractions that Leo can afford with his $15 budget:

(1 point)
Responses

0 food items and 8 attractions
0 food items and 8 attractions

2 food items and 4 attractions
2 food items and 4 attractions

1 food item and 5 attractions
1 food item and 5 attractions

3 food items and 2 attractions

Answer 1

To determine which combination of food items and attractions Leo can afford with his $15 budget, we can evaluate each option using the expression for total cost, \(4a + 2b\), where \(a\) is the number of food items and \(b\) is the number of attractions.

1. 0 food items and 8 attractions: \[ 4(0) + 2(8) = 0 + 16 = 16 \quad \text{(not affordable)} \]

2. 2 food items and 4 attractions: \[ 4(2) + 2(4) = 8 + 8 = 16 \quad \text{(not affordable)} \]

3. 1 food item and 5 attractions: \[ 4(1) + 2(5) = 4 + 10 = 14 \quad \text{(affordable)} \]

4. 3 food items and 2 attractions: \[ 4(3) + 2(2) = 12 + 4 = 16 \quad \text{(not affordable)} \]

Based on this analysis, the only combination that Leo can afford is: 1 food item and 5 attractions.

Answer 2

Given that f(x)is a one-to-one function and f(1)=−3, f(5)=6, and f(3)=5, find f^−1(5)

Answer 3

To find \( f^{-1}(5) \) for the one-to-one function \( f(x) \), we need to identify which input \( x \) corresponds to the output \( 5 \).

From the given information:

• \( f(1) = -3 \)
• \( f(5) = 6 \)
• \( f(3) = 5 \)

We see that:

\[ f(3) = 5 \]

Therefore, the input that gives an output of \( 5 \) is \( 3 \). This means that:

\[ f^{-1}(5) = 3 \]

So, the answer is:

\[ f^{-1}(5) = 3 \]