Question

Given: the function defined by f(x)=3x^2-4 Which statement is true? 1. f(0) = 0 2. f(-2) = f(2) 3. f(5)+ f(2) = f(7) 4. f(5) x f(2) = f(10)

Answer 1

`f(x)=3x^2-4 \\ \Downarrow \\ f(0)=3 * 0^2-4=0-4=-4 \\ -4 \\ot= 0 \\ f(0) \\ot= 0 \\ \hbox{statement 1 is false} \\ \\ f(-2)=3 * (-2)^2-4 =3 * 4-4=12-4=8 \\ f(2)=3 * 2^2-4=3 * 4-4=12-4=8 \\ 8=8 \\ f(-2)=f(2) \\ \hbox{statement 2 is true}`


`f(5)=3 * 5^2-4=3 * 25-4=75-4=71 \\ f(2)=8 \\ f(7)=3 * 7^2-4=3 * 49-4=147-4=143 \\ 71+8 \\ot= 143 \\ f(5)+f(2) \\ot= f(7) \\ \hbox{statement 3 is false} \\ \\ f(5)=71 \\ f(2)=8 \\ f(10)=3 * 10^2-4=3 * 100-4=300-4=296 \\ 71 * 8 \\ot= 296 \\ f(5) * f(2) \\ot= f(10) \\ \hbox{statement 4 is false}`

Stamement 2. f(-2)=f(2) is true.