Question

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Answer 1

Statement 1 & Statement 3

Explanation:

4 ÷ 10/3

4 × 3/10

12/10

6/5

f(x + 1) = (6/5) × f(x)

f(x) = (10/3) × (6/5)^(x-1)

f(x) = (10/3) × (5/6) × (6/5)^x

f(x) = (25/9) × (6/5)^x

The domain is all natural numbers and the range is real numbers

Answer 2

Explanation:

Step 1: Find the correct answer

Option A is correct because if you plug in the numbers...

`f(0 + 1) = (10)/(3)` →
`f(1)=(10)/(3)`

`f(1 + 1) = (6)/(5) * (10)/(3)` →
`f(2)=4`

`f(2 + 1) = (6)/(5) * (4)/(1)` →
`f(3) = (24)/(5)`

`f(3 + 1) = (6)/(5) * (24)/(5)` →
`f(4) = (144)/(25)`

Also, Option C is correct because if you plug in the numbers...

`f(1) = (10)/(3)((6)/(5))^(^1^-^1^)` →
`f(1) = (10)/(3) * 1` →
`f(1)=(10)/(3)`

`f(2) = (10)/(3)((6)/(5))^(^2^-^1^)` →
`f(2) = (10)/(3)*(6)/(5)` →
`f(2) = 4`

`f(3) = (10)/(3)((6)/(5))^(^3^-^1^)` →
`f(3) = (10)/(3)*(36)/(25)` →
`f(3) = (24)/(5)`

`f(4) = (10)/(3)((6)/(5))^(^4^-^1^)` →
`f(4) = (10)/(3) * (216)/(125)` →
`f(4) = (144)/(25)`

The reason why option B is not correct is because when you plug in a number, the output is incorrect. The reason why Option D is not correct is because the domain does not include negative numbers which means that the domain is all natural numbers. The reason why Option E is not correct is because the range is all real numbers and not just natural/positive numbers.

Answer: Options A, C