Question

Using f(x) =x^2/3-2, determine if each statement below is true or false. Show the work that justifies your answer. The statements are A. F(6)=f(-6) B. F(6)=2 • f(3)

Answer 1

`f(6) = f(-6)` --- True

`f(6)=2 * f(3)` --- False

Explanation:

Given

`f(x) = (x^2)/(3) - 2`

Solving (a): f(6) = f(-6)

First, we solve for f(6) by substituting 6 for x in
`f(x) = (x^2)/(3) - 2`

`f(6) = (6^2)/(3) - 2`

`f(6) = (36)/(3) - 2`

`f(6) = 12 - 2`

`f(6) = 10`

Next, we solve for f(-6) by substituting -6 for x in
`f(x) = (x^2)/(3) - 2`

`f(-6) = (-6^2)/(3) - 2`

`f(-6) = (36)/(3) - 2`

`f(-6) = 12 - 2`

`f(-6) = 10`

We have that:

`f(6) = f(-6) = 10`

Hence, the statement is true

Solving (b):
`f(6)=2 * f(3)`

We have that:

`f(6) = 10`

Next, we solve for f(3) by substituting 3 for x in
`f(x) = (x^2)/(3) - 2`

`f(3) = (3^2)/(3) - 2`

`f(3) = (9)/(3) - 2`

`f(3) = 3 - 2`

`f(3) = 1`

`2 * f(3) = 2 * 1`

`2 * f(3) = 2`

So:

`f(6)=2 * f(3)`

`10 \\eq 2`

Hence, the statement is false