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given the function f defined by f(x)=3x^2-4. which statement is true

1. f(0)= 0
2. f(-2)= f(2)
3. f(2) + f(5) = f(7)
4. f(5) x f(2) = f(10)

PLEASE EXPLAIN

Sagot :

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ok so

here i am
woot

f(2) basically means substituting the value of x in the equation with a number 2
f(5) would mean subs x with a 5 
and so on and so on until 
i think u'll get it :)
calculista

we will proceed to solve each case to determine the solution

we have

[tex]f(x)=3x^2-4[/tex]

case 1) f(0)= 0

For [tex]x=0[/tex]

Find the value of f(x)

[tex]f(0)=3*0^2-4[/tex]

[tex]f(0)=-4[/tex]

so

[tex]f(0)\neq 0[/tex]

therefore

the statement case 1) is false

case 2) f(-2)= f(2)

For [tex]x=-2[/tex]

Find the value of f(x)

[tex]f(-2)=3*(-2)^2-4[/tex]

[tex]f(-2)=8[/tex]

For [tex]x=2[/tex]

Find the value of f(x)

[tex]f(2)=3*(2)^2-4[/tex]

[tex]f(2)=8[/tex]

so

[tex]f(-2)=f(2)[/tex]

therefore

the statement case 2) is true

case 3)  f(2) + f(5) = f(7)

For [tex]x=2[/tex]

Find the value of f(x)

[tex]f(2)=3*(2)^2-4[/tex]

[tex]f(2)=8[/tex]

For [tex]x=5[/tex]

Find the value of f(x)

[tex]f(5)=3*(5)^2-4[/tex]

[tex]f(5)=71[/tex]

For [tex]x=7[/tex]

Find the value of f(x)

[tex]f(7)=3*(7)^2-4[/tex]

[tex]f(7)=143[/tex]

so

[tex]f(2)+f(5)\neq f(7)[/tex]

therefore

the statement case 3) is false

case 4) f(5) x f(2) = f(10)

For [tex]x=5[/tex]

Find the value of f(x)

[tex]f(5)=3*(5)^2-4[/tex]

[tex]f(5)=71[/tex]

For [tex]x=2[/tex]

Find the value of f(x)

[tex]f(2)=3*(2)^2-4[/tex]

[tex]f(2)=8[/tex]

For [tex]x=10[/tex]

Find the value of f(x)

[tex]f(10)=3*(10)^2-4[/tex]

[tex]f(10)=296[/tex]

so

[tex]f(5)*f(2)\neq f(10)[/tex]

therefore

the statement case 4) is false


The answer is

[tex]f(-2)= f(2)[/tex]

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