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

Answer:

$f(6) = f(-6)$ --- True

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

Step-by-step explanation:

Given

$f(x) = \frac{x^2}{3} - 2$

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

First, we solve for f(6) by substituting 6 for x in $f(x) = \frac{x^2}{3} - 2$

$f(6) = \frac{6^2}{3} - 2$

$f(6) = \frac{36}{3} - 2$

$f(6) = 12 - 2$

$f(6) = 10$

Next, we solve for f(-6) by substituting -6 for x in $f(x) = \frac{x^2}{3} - 2$

$f(-6) = \frac{-6^2}{3} - 2$

$f(-6) = \frac{36}{3} - 2$

$f(-6) = 12 - 2$

$f(-6) = 10$

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 $f(x) = \frac{x^2}{3} - 2$

$f(3) = \frac{3^2}{3} - 2$

$f(3) = \frac{9}{3} - 2$

$f(3) = 3 - 2$

$f(3) = 1$

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

$2 * f(3) = 2$

So:

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

$10 \neq 2$

Hence, the statement is false