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

$f(x)=3x^2-4 \\ \Downarrow \\ f(0)=3 \times 0^2-4=0-4=-4 \\ -4 \not= 0 \\ f(0) \not= 0 \\ \hbox{statement 1 is false} \\ \\ f(-2)=3 \times (-2)^2-4 =3 \times 4-4=12-4=8 \\ f(2)=3 \times 2^2-4=3 \times 4-4=12-4=8 \\ 8=8 \\ f(-2)=f(2) \\ \hbox{statement 2 is true}$

$f(5)=3 \times 5^2-4=3 \times 25-4=75-4=71 \\ f(2)=8 \\ f(7)=3 \times 7^2-4=3 \times 49-4=147-4=143 \\ 71+8 \not= 143 \\ f(5)+f(2) \not= f(7) \\ \hbox{statement 3 is false} \\ \\ f(5)=71 \\ f(2)=8 \\ f(10)=3 \times 10^2-4=3 \times 100-4=300-4=296 \\ 71 \times 8 \not= 296 \\ f(5) \times f(2) \not= f(10) \\ \hbox{statement 4 is false}$

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