Answered

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

Verified Answer :

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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

\(f(x)=3x^2-4\)

case 1) f(0)= 0

For \(x=0\)

Find the value of f(x)

\(f(0)=3*0^2-4\)

\(f(0)=-4\)

so

\(f(0) eq 0\)

therefore

the statement case 1) is false

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

For \(x=-2\)

Find the value of f(x)

\(f(-2)=3*(-2)^2-4\)

\(f(-2)=8\)

For \(x=2\)

Find the value of f(x)

\(f(2)=3*(2)^2-4\)

\(f(2)=8\)

so

\(f(-2)=f(2)\)

therefore

the statement case 2) is true

case 3)  f(2) + f(5) = f(7)

For \(x=2\)

Find the value of f(x)

\(f(2)=3*(2)^2-4\)

\(f(2)=8\)

For \(x=5\)

Find the value of f(x)

\(f(5)=3*(5)^2-4\)

\(f(5)=71\)

For \(x=7\)

Find the value of f(x)

\(f(7)=3*(7)^2-4\)

\(f(7)=143\)

so

\(f(2)+f(5) eq f(7)\)

therefore

the statement case 3) is false

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

For \(x=5\)

Find the value of f(x)

\(f(5)=3*(5)^2-4\)

\(f(5)=71\)

For \(x=2\)

Find the value of f(x)

\(f(2)=3*(2)^2-4\)

\(f(2)=8\)

For \(x=10\)

Find the value of f(x)

\(f(10)=3*(10)^2-4\)

\(f(10)=296\)

so

\(f(5)*f(2) eq f(10)\)

therefore

the statement case 4) is false


The answer is

\(f(-2)= f(2)\)

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