5. for ( f(x)=4 x^{2}+2 x ), find all the values of ( x ) a. ( f(2)-f(4) )

Explanation:

Step1: Calculate ( f(2) )

Substitute ( x = 2 ) into ( f(x)=4x^{2}+2x ). [ \begin{align*} f(2)&=4\times(2)^{2}+2\times2\ &=4\times4 + 4\ &=16+4\ &=20 \end{align*} ]

Step2: Calculate ( f(4) )

Substitute ( x = 4 ) into ( f(x)=4x^{2}+2x ). [ \begin{align*} f(4)&=4\times(4)^{2}+2\times4\ &=4\times16+8\ &=64 + 8\ &=72 \end{align*} ]

Step3: Calculate ( f(2)-f(4) )

[ \begin{align*} f(2)-f(4)&=20 - 72\ &=- 52 \end{align*} ]

Answer:

(-52)